1. Near-Optimal Task Selection with Mutual Information for Meta-Learning.
   Yizhou Chen, Shizhuo Zhang & Kian Hsiang Low.
   In Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS-22), Mar 28 - 30, 2022.
   29.2% acceptance rate
   
   
   Abstract. This paper addresses the problem of active task selection which involves selecting the most informative tasks for meta-learning. We propose a novel active task selection criterion based on the mutual information between latent task vectors. Unfortunately, such a criterion scales poorly in the number of candidate tasks when optimized. To resolve this issue, we exploit the submodularity property of our new criterion for devising the first active task selection algorithm for meta-learning with a near-optimal performance guarantee. To further improve the efficiency of our algorithm, we propose an online variant of the Stein variational gradient descent to perform fast belief updates of the meta-parameters via maintaining a set of forward (and backward) particles when learning (or unlearning) from each selected task. We empirically demonstrate the performance of our proposed algorithm on real-world datasets.
   
   
2. Incentivizing Collaboration in Machine Learning via Synthetic Data Rewards.
   Sebastian Tay, Xinyi Xu, Chuan Sheng Foo & Kian Hsiang Low.
   In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI-22), Feb 22 - Mar 1, 2022.
   15% acceptance rate
   
   
   Abstract. This paper presents a novel collaborative generative modeling (CGM) framework that incentivizes collaboration among self-interested parties to contribute data to a pool for training a generative model (e.g., GAN), from which synthetic data are drawn and distributed to the parties as rewards commensurate to their contributions. Distributing synthetic data as rewards (instead of trained models or money) offers task- and model-agnostic benefits for downstream learning tasks and is less likely to violate data privacy regulation. To realize the framework, we firstly propose a data valuation function using maximum mean discrepancy (MMD) that values data based on its quantity and quality in terms of its closeness to the true data distribution and provide theoretical results guiding the kernel choice in our MMD-based data valuation function. Then, we formulate the reward scheme as a linear optimization problem that when solved, guarantees certain incentives such as fairness in the CGM framework. We devise a weighted sampling algorithm for generating synthetic data to be distributed to each party as reward such that the value of its data and the synthetic data combined matches its assigned reward value by the reward scheme. We empirically show using simulated and real-world datasets that the parties' synthetic data rewards are commensurate to their contributions.
   
   
3. Differentially Private Federated Bayesian Optimization with Distributed Exploration.
   Zhongxiang Dai, Kian Hsiang Low & Patrick Jaillet.
   In Advances in Neural Information Processing Systems 34: 35th Annual Conference on Neural Information Processing Systems (NeurIPS'21), Dec 6-14, 2021.
   25.6% acceptance rate
   
   
   Abstract. Bayesian optimization (BO) has recently been extended to the federated learning (FL) setting by the federated Thompson sampling (FTS) algorithm. However, FTS is not equipped with a rigorous privacy guarantee which is an important consideration in FL. Recent works have incorporated differential privacy (DP) into the training of deep neural networks through a general framework for adding DP to iterative algorithms. Following this general DP framework, our work here integrates DP into FTS to preserve user-level privacy. We also leverage the ability of this general DP framework to handle different parameter vectors, as well as the technique of local modeling for BO, to further improve the utility of our algorithm through distributed exploration (DE). The resulting differentially private FTS with DE (DP-FTS-DE) algorithm is endowed with theoretical guarantees for both the privacy and utility and is amenable to interesting theoretical insights about the privacy-utility trade-off. We also use real-world experiments to show that DP-FTS-DE achieves high utility (competitive performance) with a strong privacy guarantee (small privacy loss) and induces a practical trade-off between privacy and utility.
   
   
4. Optimizing Conditional Value-At-Risk of Black-Box Functions.
   Quoc Phong Nguyen, Zhongxiang Dai, Kian Hsiang Low & Patrick Jaillet.
   In Advances in Neural Information Processing Systems 34: 35th Annual Conference on Neural Information Processing Systems (NeurIPS'21), Dec 6-14, 2021.
   25.6% acceptance rate
   
   
   Abstract. This paper presents two Bayesian optimization (BO) algorithms with theoretical performance guarantee to maximize the conditional value-at-risk (CVaR) of a black-box function: CV-UCB and CV-TS which are based on the well-established principle of optimism in the face of uncertainty and Thompson sampling, respectively. To achieve this, we develop an upper confidence bound of CVaR and prove the no-regret guarantee of CV-UCB by utilizing an interesting connection between CVaR and value-at-risk (VaR). For CV-TS, though it is straightforwardly performed with Thompson sampling, bounding its Bayesian regret is non-trivial because it requires a tail expectation bound for the distribution of CVaR of a black-box function, which has not been shown in the literature. The performances of both CV-UCB and CV-TS are empirically evaluated in optimizing CVaR of synthetic benchmark functions and simulated real-world optimization problems.
   
   
5. Fault-Tolerant Federated Reinforcement Learning with Theoretical Guarantee.
   Xiaofeng Fan, Yining Ma, Zhongxiang Dai, Wei Jing, Cheston Tan & Kian Hsiang Low.
   In Advances in Neural Information Processing Systems 34: 35th Annual Conference on Neural Information Processing Systems (NeurIPS'21), Dec 6-14, 2021.
   25.6% acceptance rate
   
   
   Abstract. The growing literature of Federated Learning (FL) has recently inspired Federated Reinforcement Learning (FRL) to encourage multiple agents to federatively build a better decision-making policy without sharing raw trajectories. Despite its promising applications, existing FRL work fails to I) provide theoretical analysis on its convergence; II) account for random system failures and adversarial attacks. Towards this end, we propose the first FRL framework, the convergence of which is tolerant to less than half of participating agents being random system failures or adversarial attackers. We prove that the sample efficiency of the proposed framework is guaranteed to scale with the number of agents, accounting for such potential failures or attacks. We empirically verify all theoretical results on various RL benchmarking tasks.
   
   
6. Gradient Driven Rewards to Guarantee Fairness in Collaborative Machine Learning.
   Xinyi Xu, Lingjuan Lyu, Xingjun Ma, Chenglin Miao, Chuan Sheng Foo & Kian Hsiang Low.
   In Advances in Neural Information Processing Systems 34: 35th Annual Conference on Neural Information Processing Systems (NeurIPS'21), Dec 6-14, 2021.
   25.6% acceptance rate
   
   
   Abstract. In collaborative machine learning (CML), multiple agents pool their resources (e.g., data) together for a common learning task. In realistic CML settings where the agents are self-interested and not altruistic, they may be unwilling to share data or model information without adequate rewards. Furthermore, as the data/model information shared by the agents may differ in quality, designing rewards which are fair to them is important so that they would not feel exploited nor discouraged from sharing. In this paper, we adopt federated learning as the CML paradigm, propose a novel cosine gradient Shapley value (CGSV) to fairly evaluate the expected marginal contribution of each agent's uploaded model parameter update/gradient without needing an auxiliary validation dataset, and based on the CGSV, design a novel training-time gradient reward mechanism with a fairness guarantee by sparsifying the aggregated parameter update/gradient downloaded from the server as reward to each agent such that its resulting quality is commensurate to that of the agent’s uploaded parameter update/gradient. We empirically demonstrate the effectiveness of our fair gradient reward mechanism on multiple benchmark datasets in terms of fairness, predictive performance, and time overhead.
   
   
7. Validation Free and Replication Robust Volume-based Data Valuation.
   Xinyi Xu, Zhaoxuan Wu, Chuan Sheng Foo & Kian Hsiang Low.
   In Advances in Neural Information Processing Systems 34: 35th Annual Conference on Neural Information Processing Systems (NeurIPS'21), Dec 6-14, 2021.
   25.6% acceptance rate
   
   
   Abstract. Data valuation arises as a non-trivial challenge in use cases such as collaborative data sharing, data markets and etc. The value of data is often related to the learning performance, e.g. validation accuracy, of the model trained on the data. While intuitive, this methodology introduces a high coupling between data valuation and validation, which may not be desirable in practice. For instance, data providers may disagree on the choice of the validation set, or the validation set may be (statistically) different from the actual application. A separate but practical issue is data replication. If some data points are valuable, a dishonest data provider may offer a dataset containing replications of these data points, trying to exploit the valuation to get a higher reward/payment. Based on the ordinary least squares framework, our data valuation method does not require validation, and still provides a useful connection between the value of data and learning performance. In particular, we utilize the volume of the data matrix (determinant of its left Gram), thus able to provide an intuitive interpretation of the value of data via the diversity in the data. Furthermore, we formalize the robustness to data replication, and propose a robust volume valuation with robustness guarantees. We conduct extensive experiments to demonstrate its consistency and practical advantages over existing baselines.
   
   

1. Learning to Learn with Gaussian Processes.
   Quoc Phong Nguyen, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 37th Conference on Uncertainty in Artificial Intelligence (UAI-21), pages 1466-1475, Jul 27-30, 2021.
   26.5% acceptance rate
   
   
   Abstract. This paper presents Gaussian process meta-learning (GPML) for few-shot regression, which explicitly exploits the distance between regression problems/tasks using a novel task kernel. It contrasts sharply with the popular metric-based meta-learning approach which is based on the distance between data inputs or their embeddings in the few-shot learning literature. Apart from the superior predictive performance by capturing the diversity of different tasks, GPML offers a set of representative tasks that are useful for understanding the task distribution. We empirically demonstrate the performance and interpretability of GPML in several few-shot regression problems involving a multimodal task distribution and real-world datasets.
   
   
2. Trusted-Maximizers Entropy Search for Efficient Bayesian Optimization.
   Quoc Phong Nguyen, Zhaoxuan Wu, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 37th Conference on Uncertainty in Artificial Intelligence (UAI-21), pages 1486-1495, Jul 27-30, 2021.
   26.5% acceptance rate
   
   
   Abstract. Information-based Bayesian optimization (BO) algorithms have achieved state-of-the-art performance in optimizing a black-box objective function. However, they usually require several approximations or simplifying assumptions (without clearly understanding their effects on the BO performance) and/or their generalization to batch BO is computationally unwieldy, especially with an increasing batch size. To alleviate these issues, this paper presents a novel trusted-maximizers entropy search (TES) acquisition function: It measures how much an input query contributes to the information gain on the maximizer over a finite set of trusted maximizers, i.e., inputs optimizing functions that are sampled from the Gaussian process posterior belief of the objective function. Evaluating TES requires either only a stochastic approximation with sampling or a deterministic approximation with expectation propagation, both of which are investigated and empirically evaluated using synthetic benchmark objective functions and real-world optimization problems, e.g., hyperparameter tuning of a convolutional neural network and synthesizing ‘physically realizable’ faces to fool a black-box face recognition system. Though TES can naturally be generalized to a batch variant with either approximation, the latter is amenable to be scaled to a much larger batch size in our experiments.
   
   
3. Collaborative Bayesian Optimization with Fair Regret.
   Rachael Hwee Ling Sim, Yehong Zhang, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 38th International Conference on Machine Learning (ICML-21), pages 9691-9701, Jul 18-24, 2021.
   21.5% acceptance rate
   
   
   Abstract. Bayesian optimization (BO) is a popular tool for optimizing complex and costly-to-evaluate black-box objective functions. To further reduce the number of function evaluations, any party performing BO may be interested to collaborate with others to optimize the same objective function concurrently. To do this, existing BO algorithms have considered optimizing a batch of input queries in parallel and provided theoretical bounds on their cumulative regret reflecting inefficiency. However, when the objective function values are correlated with real-world rewards (e.g., money), parties may be hesitant to collaborate if they risk incurring larger cumulative regret (i.e., smaller real-world reward) than others. This paper shows that fairness and efficiency are both necessary for the collaborative BO setting. Inspired by social welfare concepts from economics, we propose a new notion of regret capturing these properties and a collaborative BO algorithm whose convergence rate can be theoretically guaranteed by bounding the new regret, both of which share an adjustable parameter for trading off between fairness vs. efficiency. We empirically demonstrate the benefits (e.g., increased fairness) of our algorithm using synthetic and real-world datasets.
   
   
4. Model Fusion for Personalized Learning.
   Chi Thanh Lam, Trong Nghia Hoang, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 38th International Conference on Machine Learning (ICML-21), pages 5948-5958, Jul 18-24, 2021.
   21.5% acceptance rate
   
   
   Abstract. Production systems operating on a growing domain of analytic services often require generating warm-start solution models for emerging tasks with limited data. One potential approach to address this challenge is to adopt meta learning to generate a base model that can be adapted to solve unseen tasks with minimal fine-tuning. This however requires the training processes of previous solution models of existing tasks to be synchronized. This is not possible if these models were pre-trained separately on private data owned by different entities and cannot be synchronously re-trained. To accommodate for such scenarios, we develop a new personalized learning framework that synthesizes customized models for unseen tasks via fusion of independently pre-trained models of related tasks. We establish performance guarantee for the proposed framework and demonstrate its effectiveness on both synthetic and real datasets.
   
   
5. Value-at-Risk Optimization with Gaussian Processes.
   Quoc Phong Nguyen, Zhongxiang Dai, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 38th International Conference on Machine Learning (ICML-21), pages 8063-8072, Jul 18-24, 2021.
   21.5% acceptance rate
   
   
   Abstract. Value-at-risk (VaR) is an established measure to assess risks in critical real-world applications with random environmental factors. This paper presents a novel VaR upper confidence bound (V-UCB) algorithm for maximizing the VaR of a black-box objective function with the first no-regret guarantee. To realize this, we first derive a confidence bound of VaR and then prove the existence of values of the environmental random variable (to be selected to achieve no regret) such that the confidence bound of VaR lies within that of the objective function evaluated at such values. Our V-UCB algorithm empirically demonstrates state-of-the-art performance in optimizing synthetic benchmark functions, a portfolio optimization problem, and a simulated robot task.
   
   
6. AID: Active Distillation Machine to Leverage Pre-Trained Black-Box Models in Private Data Settings.
   Trong Nghia Hoang, Shenda Hong, Cao Xiao, Kian Hsiang Low & Jimeng Sun.
   In Proceedings of the 30th The Web Conference (WWW'21), pages 3569–3581, Apr 19-23, 2021.
   20.6% acceptance rate
   
   
   Abstract. This paper presents an active distillation method for a local institution (e.g., hospital) to find the best queries within its given budget to distill an on-server black-box model's predictive knowledge into a local surrogate with transparent parameterization. This allows local institutions to understand better the predictive reasoning of the black-box model in its own local context or to further customize the distilled knowledge with its private dataset that cannot be centralized and fed into the server model. The proposed method thus addresses several challenges of deploying machine learning in many industrial settings (e.g., healthcare analytics) with strong proprietary constraints. These include: (1) the opaqueness of the server model’s architecture which prevents local users from understanding its predictive reasoning in their local data contexts; (2) the increasing cost and risk of uploading local data on the cloud for analysis; and (3) the need to customize the server model with private onsite data. We evaluated the proposed method on both benchmark and real-world healthcare data where significant improvements over existing local distillation methods were observed. A theoretical analysis of the proposed method is also presented.
   
   
7. Top-k Ranking Bayesian Optimization.
   Quoc Phong Nguyen, Sebastian Tay, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI-21), pages 9135-9143, Feb 2-9, 2021.
   21.4% acceptance rate
   
   
   Abstract. This paper presents a novel approach to top-k ranking Bayesian optimization (top-k ranking BO) which is a practical and significant generalization of preferential BO to handle top-k ranking and tie/indifference observations. We first design a surrogate model that is not only capable of catering to the above observations, but is also supported by a classic random utility model. Another equally important contribution is the introduction of the first information-theoretic acquisition function in BO with preferential observation called multinomial predictive entropy search (MPES) which is flexible in handling these observations and optimized for all inputs of a query jointly. MPES possesses superior performance compared with existing acquisition functions that select the inputs of a query one at a time greedily. We empirically evaluate the performance of MPES using several synthetic benchmark functions, CIFAR-10 dataset, and SUSHI preference dataset.
   
   
8. An Information-Theoretic Framework for Unifying Active Learning Problems.
   Quoc Phong Nguyen, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI-21), pages 9126-9134, Feb 2-9, 2021.
   21.4% acceptance rate
   
   
   Abstract. This paper presents an information-theoretic framework for unifying active learning problems: level set estimation (LSE), Bayesian optimization (BO), and their generalized variant. We first introduce a novel active learning criterion that subsumes an existing LSE algorithm and achieves state-of-the-art performance in LSE problems with a continuous input domain. Then, by exploiting the relationship between LSE and BO, we design a competitive information-theoretic acquisition function for BO that has interesting connections to upper confidence bound and max-value entropy search (MES). The latter connection reveals a drawback of MES which has important implications on not only MES but also on other MES-based acquisition functions. Finally, our unifying information-theoretic framework can be applied to solve a generalized problem of LSE and BO involving multiple level sets in a data-efficient manner. We empirically evaluate the performance of our proposed algorithms using synthetic benchmark functions, a real-world dataset, and in hyperparameter tuning of machine learning models.
   
   
9. Convolutional Normalizing Flows for Deep Gaussian Processes.
   Haibin Yu, Dapeng Liu, Kian Hsiang Low & Patrick Jaillet.
   In Proceedings of the International Joint Conference on Neural Networks (IJCNN'21), Jul 18-22, 2021.
   
   
   
   Abstract. Deep Gaussian processes (DGPs), a hierarchical composition of GP models, have successfully boosted the expressive power of their single-layer counterpart. However, it is impossible to perform exact inference in DGPs, which has motivated the recent development of variational inference-based methods. Unfortunately, either these methods yield a biased posterior belief or it is difficult to evaluate their convergence. This paper introduces a new approach for specifying flexible, arbitrarily complex, and scalable approximate posterior distributions. The posterior distribution is constructed through a normalizing flow (NF) which transforms a simple initial probability into a more complex one through a sequence of invertible transformations. Moreover, a novel convolutional normalizing flow (CNF) is developed to improve the time efficiency and capture dependency between layers. Empirical evaluation shows that CNF DGP outperforms the state-of-the-art approximation methods for DGPs.
   
   
10. Efficient Exploration of Reward Functions in Inverse Reinforcement Learning via Bayesian Optimization.
    Sreejith Balakrishnan, Quoc Phong Nguyen, Kian Hsiang Low & Harold Soh.
    In Advances in Neural Information Processing Systems 33: 34th Annual Conference on Neural Information Processing Systems (NeurIPS'20), pages 4187-4198, Dec 6-12, 2020.
    20.1% acceptance rate
    
    
    Abstract. In this paper, we focus on the problem of Inverse Reinforcement Learning (IRL), which is relevant for a variety of tasks including value alignment and robot learning from demonstration. Despite significant algorithmic contributions in recent years, IRL remains an ill-posed problem at its core; multiple reward functions coincide with the observed behavior, and the actual reward function is not identifiable without prior knowledge or supplementary information. Here, we propose Bayesian Optimization-IRL (BO-IRL), an IRL framework that identifies multiple solutions that are consistent with the expert demonstrations by efficiently exploring the reward function space. BO-IRL achieves this by utilizing Bayesian Optimization along with our newly proposed kernel that (a) projects the parameters of policy invariant reward functions to a single point in a latent space, and (b) ensures that nearby points in the latent space correspond to reward functions that yield similar likelihoods. This projection allows for the use of standard stationary kernels in the latent space to capture the correlations present across the reward function space. Empirical results on synthetic and real-world environments (model-free and model-based) show that BO-IRL discovers multiple reward functions while minimizing the number of expensive exact policy optimizations.
    
    
11. Federated Bayesian Optimization via Thompson Sampling.
    Zhongxiang Dai, Kian Hsiang Low & Patrick Jaillet.
    In Advances in Neural Information Processing Systems 33: 34th Annual Conference on Neural Information Processing Systems (NeurIPS'20), pages 9687-9699, Dec 6-12, 2020.
    20.1% acceptance rate
    
    
    Abstract. Bayesian optimization (BO) is a prominent method for optimizing expensive-to-compute black-box functions. The massive computational capability of edge devices such as mobile phones, coupled with privacy concerns, has led to immense recent interest in federated learning (FL), which focuses on collaborative training of deep neural networks (DNN) via first-order optimization techniques. However, some common machine learning tasks such as hyperparameter tuning of DNN lack access to gradients and thus require zeroth-order optimization (black-box optimization). This hints at the considerable potential of extending BO to the FL setting (FBO), to allow agents to collaborate in these black-box optimization tasks. Here, we introduce federated Thompson sampling (FTS), which overcomes a number of key challenges of FBO and FL in a principled way: We (a) use random Fourier features to approximate the Gaussian process surrogate model used in BO which naturally produces the parameters to be exchanged between agents, (b) design FTS based on Thompson sampling which significantly reduces the number of parameters to be exchanged, and (c) provide a theoretical convergence guarantee that is robust against heterogeneous agents which is a major challenge in FL and FBO. We empirically demonstrate the effectiveness of FTS in terms of communication efficiency, computational efficiency and practical performance.
    
    
12. Variational Bayesian Unlearning.
    Quoc Phong Nguyen, Kian Hsiang Low & Patrick Jaillet.
    In Advances in Neural Information Processing Systems 33: 34th Annual Conference on Neural Information Processing Systems (NeurIPS'20), pages 16025-16036, Dec 6-12, 2020.
    20.1% acceptance rate
    
    
    Abstract. This paper studies the problem of approximately unlearning a Bayesian model from a small subset of the training data to be erased. We frame this problem as one of minimizing the Kullback-Leibler distance between the approximate posterior belief of model parameters after directly unlearning from the erased data vs. the exact posterior belief from retraining with remaining data. Using the variational inference (VI) framework, we show that it is equivalent to minimizing an evidence upper bound which trades off between fully unlearning from erased data vs. not entirely forgetting the posterior belief given the full data (i.e., including the remaining data); the latter prevents catastrophic unlearning that can render the model useless. In model training with VI, only an approximate (instead of exact) posterior belief given the full data can be obtained, which makes unlearning even more challenging. We propose two novel tricks to tackle this challenge. We empirically demonstrate our unlearning methods on Bayesian models such as sparse Gaussian process and logistic regression using synthetic and real-world datasets.
    
    
13. Collaborative Machine Learning with Incentive-Aware Model Rewards.
    Rachael Hwee Ling Sim, Yehong Zhang, Mun Choon Chan & Kian Hsiang Low.
    In Proceedings of the 37th International Conference on Machine Learning (ICML-20), pages 8927-8936, Jun 12-18, 2020.
    21.8% acceptance rate
    
    
    Abstract. Collaborative machine learning (ML) is an appealing paradigm to build high-quality ML models by training on the aggregated data from many parties. However, these parties are only willing to share their data when given enough incentives, such as a guaranteed fair reward based on their contributions. This motivates the need for measuring a party's contribution and designing an incentive-aware reward scheme accordingly. This paper proposes to value a party's reward based on Shapley value and information gain on model parameters given its data. Subsequently, we give each party a model as a reward. To formally incentivize the collaboration, we define some desirable properties (e.g., fairness and stability) which are inspired by cooperative game theory but adapted for our model reward that is uniquely freely replicable. Then, we propose a novel model reward scheme to satisfy fairness and trade off between the desirable properties via an adjustable parameter. The value of each party's model reward determined by our scheme is attained by injecting Gaussian noise to the aggregated training data with an optimized noise variance. We empirically demonstrate interesting properties of our scheme and evaluate its performance using synthetic and real-world datasets.
    
    
14. R2-B2: Recursive Reasoning-Based Bayesian Optimization for No-Regret Learning in Games.
    Zhongxiang Dai, Yizhou Chen, Kian Hsiang Low, Patrick Jaillet & Teck-Hua Ho.
    In Proceedings of the 37th International Conference on Machine Learning (ICML-20), pages 2291-2301, Jun 12-18, 2020.
    21.8% acceptance rate
    
    
    Abstract. This paper presents a recursive reasoning formalism of Bayesian optimization (BO) to model the reasoning process in the interactions between boundedly rational, self-interested agents with unknown, complex, and costly-to-evaluate payoff functions in repeated games, which we call Recursive Reasoning-Based BO (R2-B2). Our R2-B2 algorithm is general in that it does not constrain the relationship among the payoff functions of different agents and can thus be applied to various types of games such as constant-sum, general-sum, and common-payoff games. We prove that by reasoning at level 2 or more and at one level higher than the other agents, our R2-B2 agent can achieve faster asymptotic convergence to no regret than that without utilizing recursive reasoning. We also propose a computationally cheaper variant of R2-B2 called R2-B2-Lite at the expense of a weaker convergence guarantee. The performance and generality of our R2-B2 algorithm are empirically demonstrated using synthetic games, adversarial machine learning, and multi-agent reinforcement learning.
    
    
15. Private Outsourced Bayesian Optimization.
    Dmitrii Kharkovskii, Zhongxiang Dai & Kian Hsiang Low.
    In Proceedings of the 37th International Conference on Machine Learning (ICML-20), pages 5231-5242, Jun 12-18, 2020.
    21.8% acceptance rate
    
    
    Abstract. This paper presents the private-outsourced-Gaussian process-upper confidence bound (PO-GP-UCB) algorithm, which is the first algorithm for privacy-preserving Bayesian optimization (BO) in the outsourced setting with a provable performance guarantee. We consider the outsourced setting where the entity holding the dataset and the entity performing BO are represented by different parties, and the dataset cannot be released non-privately. For example, a hospital holds a dataset of sensitive medical records and outsources the BO task on this dataset to an industrial AI company. The key idea of our approach is to make the BO performance of our algorithm similar to that of non-private GP-UCB run using the original dataset, which is achieved by using a random projection-based transformation that preserves both privacy and the pairwise distances between inputs. Our main theoretical contribution is to show that a regret bound similar to that of the standard GP-UCB algorithm can be established for our PO-GP-UCB algorithm. We empirically evaluate the performance of our PO-GP-UCB algorithm with synthetic and real-world datasets.
    
    
16. Learning Task-Agnostic Embedding of Multiple Black-Box Experts for Multi-Task Model Fusion.
    Trong Nghia Hoang, Chi Thanh Lam, Kian Hsiang Low & Patrick Jaillet.
    In Proceedings of the 37th International Conference on Machine Learning (ICML-20), pages 4282-4292, Jun 12-18, 2020.
    21.8% acceptance rate
    
    
    Abstract. Model fusion is an emerging study in collective learning where heterogeneous experts with private data and learning architectures need to combine their black-box knowledge for better performance. Existing literature achieves this via a local knowledge distillation scheme that transfuses the predictive patterns of each pre-trained expert onto a white-box imitator model, which can be incorporated efficiently into a global model. This scheme however does not extend to multi-task scenarios where different experts were trained to solve different tasks and only part of their distilled knowledge is relevant to a new task. To address this multi-task challenge, we develop a new fusion paradigm that represents each expert as a distribution over a spectrum of predictive prototypes, which are isolated from task-specific information encoded within the prototype distribution. The task-agnostic prototypes can then be reintegrated to generate a new model that solves a new task encoded with a different prototype distribution. The fusion and adaptation performance of the proposed framework is demonstrated empirically on several real-world benchmark datasets.
    
    
17. Nonmyopic Gaussian Process Optimization with Macro-Actions.
    Dmitrii Kharkovskii, Chun Kai Ling & Kian Hsiang Low.
    In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS-20), pages 4593-4604, Aug 26-28, 2020.
    28.7% acceptance rate
    
    
    Abstract. This paper presents a multi-staged approach to nonmyopic adaptive Gaussian process optimization (GPO) for Bayesian optimization (BO) of unknown, highly complex objective functions that, in contrast to existing nonmyopic adaptive BO algorithms, exploits the notion of macro-actions for scaling up to a further lookahead to match up to a larger available budget. To achieve this, we generalize GP upper confidence bound to a new acquisition function defined w.r.t. a nonmyopic adaptive macro-action policy, which is intractable to be optimized exactly due to an uncountable set of candidate outputs. The contribution of our work here is thus to derive a nonmyopic adaptive ϵ-Bayes-optimal macro-action GPO (ϵ-Macro-GPO) policy. To perform nonmyopic adaptive BO in real time, we then propose an asymptotically optimal anytime variant of our ϵ-Macro-GPO policy with a performance guarantee. We empirically evaluate the performance of our ϵ-Macro-GPO policy and its anytime variant in BO with synthetic and real-world datasets.
    
    
18. Scalable Variational Bayesian Kernel Selection for Sparse Gaussian Process Regression.
    Tong Teng, Jie Chen, Yehong Zhang & Kian Hsiang Low.
    In Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI-20), pages 5997-6004, New York, NY, Feb 7-12, 2020.
    20.6% acceptance rate
    
    
    Abstract. This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framework for SGPR models where its posterior belief is learned together with that of the other variational variables (i.e., inducing variables and kernel hyperparameters). In particular, we transform the discrete kernel belief into a continuous parametric distribution via reparameterization in order to apply VI. Though it is computationally challenging to jointly optimize a large number of hyperparameters due to many kernels being evaluated simultaneously by our VBKS algorithm, we show that the variational lower bound of the log-marginal likelihood can be decomposed into an additive form such that each additive term depends only on a disjoint subset of the variational variables and can thus be optimized independently. Stochastic optimization is then used to maximize the variational lower bound by iteratively improving the variational approximation of the exact posterior belief via stochastic gradient ascent, which incurs constant time per iteration and hence scales to big data. We empirically evaluate the performance of our VBKS algorithm on synthetic and massive real-world datasets.
    
    
19. Gaussian Process Decentralized Data Fusion Meets Transfer Learning in Large-Scale Distributed Cooperative Perception.
    Ruofei Ouyang & Kian Hsiang Low.
    In Autonomous Robots (Special Issue on Multi-Robot and Multi-Agent Systems), volume 44, issue 3, pages 359-376, March 2020.
    Extended version of our AAAI-18 paper
    
    
    Abstract. This paper presents novel Gaussian process decentralized data fusion algorithms exploiting the notion of agent-centric support sets for distributed cooperative perception of large-scale environmental phenomena. To overcome the limitations of scale in existing works, our proposed algorithms allow every mobile sensing agent to utilize a different support set and dynamically switch to another during execution for encapsulating its own data into a local summary that, perhaps surprisingly, can still be assimilated with the other agents' local summaries (i.e., based on their current choices of support sets) into a globally consistent summary to be used for predicting the phenomenon. To achieve this, we propose a novel transfer learning mechanism for a team of agents capable of sharing and transferring information encapsulated in a summary based on a support set to that utilizing a different support set with some loss that can be theoretically bounded and analyzed. To alleviate the issue of information loss accumulating over multiple instances of transfer learning, we propose a new information sharing mechanism to be incorporated into our algorithms in order to achieve memory-efficient lazy transfer learning. Empirical evaluation on three real-world datasets for up to 128 agents show that our algorithms outperform the state-of-the-art methods.
    
    
20. FCM-Sketch: Generic Network Measurements with Data Plane Support.
    Cha Hwan Song, Pravein Govindan Kannan, Kian Hsiang Low & Mun Choon Chan.
    In Proceedings of the 16th International Conference on emerging Networking EXperiments and Technologies (CoNEXT'20), pages 78-92, Dec 1-4, 2020.
    24% acceptance rate
    
    
    Abstract. Sketches have successfully provided accurate and fine-grained measurements (e.g., flow size and heavy hitters) which are imperative for network management. In particular, Count-Min (CM) sketch is widely utilized in many applications due to its simple design and ease of implementation. There have been many efforts to build monitoring frameworks based on Count-Min sketch. However, these frameworks either support very specific measurement tasks or they cannot be implemented on high-speed programmable hardware (PISA). In this work, we propose FCM, a framework that is designed to support generic network measurement with high accuracy. Our key contribution is FCM-Sketch, a data structure that has a lightweight implementation on the emerging PISA programmable switches. FCM-Sketch can also be used as a substitute for CM-Sketch in applications that use CM-Sketch. We have implemented FCM-Sketch on a commodity programmable switch (Barefoot Tofino) using the P4 language. Our evaluation shows that FCM-Sketch can reduce the errors in many measurement tasks by 50% to 80% compared to CM-Sketch and other state-of-the-art approaches.
    
    
21. Implicit Posterior Variational Inference for Deep Gaussian Processes.
    Haibin Yu, Yizhou Chen, Zhongxiang Dai, Kian Hsiang Low & Patrick Jaillet.
    In Advances in Neural Information Processing Systems 32: 33rd Annual Conference on Neural Information Processing Systems (NeurIPS'19), pages 14475-14486, Vancouver, Canada, Dec 7-12, 2019.
    3% acceptance rate (spotlight presentation)
    
    
    Abstract. A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. This paper presents an implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework achieves this by casting the DGP inference problem as a two-player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief. This consequently inspires us to devise a best-response dynamics algorithm to search for a Nash equilibrium (i.e., an unbiased posterior belief). Empirical evaluation shows that IPVI outperforms the state-of-the-art approximation methods for DGPs.
    
    
22. Bayesian Optimization with Binary Auxiliary Information.
    Yehong Zhang, Zhongxiang Dai & Kian Hsiang Low.
    In Proceedings of the 35th Conference on Uncertainty in Artificial Intelligence (UAI-19), pages 1222-1232, Tel Aviv, Israel, Jul 22-25, 2019.
    26.2% acceptance rate (plenary talk)
    Subsumes our work on Information-Based Multi-Fidelity Bayesian Optimization presented in NeurIPS'17 Workshop on Bayesian Optimization, Long Beach, CA, Dec 9, 2017.
    
    
    Abstract. This paper presents novel mixed-type Bayesian optimization (BO) algorithms to accelerate the optimization of a target objective function by exploiting correlated auxiliary information of binary type that can be more cheaply obtained, such as in policy search for reinforcement learning and hyperparameter tuning of machine learning models with early stopping. To achieve this, we first propose a mixed-type multi-output Gaussian process (MOGP) to jointly model the continuous target function and binary auxiliary functions. Then, we propose information-based acquisition functions such as mixed-type entropy search (MT-ES) and mixed-type predictive ES (MT-PES) for mixed-type BO based on the MOGP predictive belief of the target and auxiliary functions. The exact acquisition functions of MT-ES and MT-PES cannot be computed in closed form and need to be approximated. We derive an efficient approximation of MT-PES via a novel mixed-type random features approximation of the MOGP model whose cross-correlation structure between the target and auxiliary functions can be exploited for improving the belief of the global target maximizer using the observations from evaluating these functions. We also propose new practical constraints to relate the global target maximizer to the binary auxiliary functions. We empirically evaluate the performance of MT-ES and MT-PES with synthetic and real-world experiments.
    
    
23. Bayesian Optimization Meets Bayesian Optimal Stopping.
    Zhongxiang Dai, Haibin Yu, Kian Hsiang Low & Patrick Jaillet.
    In Proceedings of the 36th International Conference on Machine Learning (ICML-19), pages 1496-1506, Long Beach, CA, Jun 9-15, 2019.
    22.6% acceptance rate
    
    
    Abstract. Bayesian optimization (BO) is a popular paradigm for optimizing the hyperparameters of machine learning (ML) models due to its sample efficiency. Many ML models require running an iterative training procedure (e.g., stochastic gradient descent). This motivates the question whether information available during the training process (e.g., validation accuracy after each epoch) can be exploited for improving the epoch efficiency of BO algorithms by early-stopping model training under hyperparameter settings that will end up under-performing and hence eliminating unnecessary training epochs. This paper proposes to unify BO (specifically, Gaussian process-upper confidence bound (GP-UCB)) with Bayesian optimal stopping (BO-BOS) to boost the epoch efficiency of BO. To achieve this, while GP-UCB is sample-efficient in the number of function evaluations, BOS complements it with epoch efficiency for each function evaluation by providing a principled optimal stopping mechanism for early stopping. BO-BOS preserves the (asymptotic) no-regret performance of GP-UCB using our specified choice of BOS parameters that is amenable to an elegant interpretation in terms of the exploration-exploitation trade-off. We empirically evaluate the performance of BO-BOS and demonstrate its generality in hyperparameter optimization of ML models and two other interesting applications.
    
    
24. Collective Model Fusion for Multiple Black-Box Experts.
    Quang Minh Hoang, Trong Nghia Hoang, Kian Hsiang Low & Carleton Kingsford.
    In Proceedings of the 36th International Conference on Machine Learning (ICML-19), pages 2742-2750, Long Beach, CA, Jun 9-15, 2019.
    22.6% acceptance rate
    
    
    Abstract. Model fusion is a fundamental problem in collective machine learning (ML) where independent experts with heterogeneous learning architectures are required to combine expertise to improve predictive performance. This is particularly challenging in information-sensitive domains (e.g., medical records in health-care analytics) where experts do not have access to each other's internal architecture and local data. To address this challenge, this paper presents the first collective model fusion framework for multiple experts with heterogeneous black-box architectures. The proposed method will enable this by addressing the following key issues of how black-box experts interact to understand the predictive behaviors of one another; how these understandings can be represented and shared efficiently among themselves; and how the shared understandings can be combined to generate high-quality consensus prediction. The performance of the resulting framework is analyzed theoretically and demonstrated empirically on several datasets.
    
    
25. Collective Online Learning of Gaussian Processes in Massive Multi-Agent Systems.
    Trong Nghia Hoang, Quang Minh Hoang, Kian Hsiang Low & Jonathan P. How.
    In Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI-19), pages 7850-7857, Honolulu, HI, Jan 27-Feb 1, 2019.
    16.2% acceptance rate (oral presentation)
    
    
    Abstract. This paper presents a novel Collective Online Learning of Gaussian Processes (COOL-GP) framework for enabling a massive number of GP inference agents to simultaneously perform (a) efficient online updates of their GP models using their local streaming data with varying correlation structures and (b) decentralized fusion of their resulting online GP models with different learned hyperparameter settings and inducing inputs. To realize this, we exploit the notion of a common encoding structure to encapsulate the local streaming data gathered by any GP inference agent into summary statistics based on our proposed representation, which is amenable to both an efficient online update via an importance sampling trick as well as multi-agent model fusion via decentralized message passing that can exploit sparse connectivity among agents for improving efficiency and enhance the robustness of our framework against transmission loss. We provide a rigorous theoretical analysis of the approximation loss arising from our proposed representation to achieve efficient online updates and model fusion. Empirical evaluations show that COOL-GP is highly effective in model fusion, resilient to information disparity between agents, robust to transmission loss, and can scale to thousands of agents.
    
    
26. Towards Robust ResNet: A Small Step but a Giant Leap.
    Jingfeng Zhang, Bo Han, Laura Wynter, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI-19), pages 4285-4291, Macao, Aug 10-16, 2019.
    17.9% acceptance rate
    
    
    Abstract. This paper presents a simple yet principled approach to boosting the robustness of the residual network (ResNet) that is motivated by the dynamical system perspective. Namely, a deep neural network can be interpreted using a partial differential equation, which naturally inspires us to characterize ResNet by an explicit Euler method. Our analytical studies reveal that the step factor h in the Euler method is able to control the robustness of ResNet in both its training and generalization. Specifically, we prove that a small step factor h can benefit the training robustness for back-propagation; from the view of forward-propagation, a small h can aid in the robustness of the model generalization. A comprehensive empirical evaluation on both vision CIFAR-10 and text AG-NEWS datasets confirms that a small h aids both the training and generalization robustness.
    
    
27. GEE: A Gradient-based Explainable Variational Autoencoder for Network Anomaly Detection.
    Quoc Phong Nguyen, Kar Wai Lim, Dinil Mon Divakaran, Kian Hsiang Low & Mun Choon Chan.
    In Proceedings of the IEEE Conference on Communications and Network Security (CNS'19), pages 91-99, Washington, DC, Jun 10-12, 2019.
    27.8% acceptance rate
    
    
    Abstract. This paper looks into the problem of detecting network anomalies by analyzing NetFlow records. While many previous works have used statistical models and machine learning techniques in a supervised way, such solutions have the limitations that they require large amount of labeled data for training and are unlikely to detect zero-day attacks. Existing anomaly detection solutions also do not provide an easy way to explain or identify attacks in the anomalous traffic. To address these limitations, we develop and present GEE, a framework for detecting and explaining anomalies in network traffic. GEE comprises of two components: (i) Variational Autoencoder (VAE) —- an unsupervised deep-learning technique for detecting anomalies, and (ii) a gradient-based fingerprinting technique for explaining anomalies. Evaluation of GEE on UGR dataset demonstrates that our approach is effective in detecting different anomalies as well as identifying fingerprints that are good representations of these various attacks.
    
    
28. Stochastic Variational Inference for Bayesian Sparse Gaussian Process Regression.
    Haibin Yu, Trong Nghia Hoang, Kian Hsiang Low & Patrick Jaillet.
    In Proceedings of the International Joint Conference on Neural Networks (IJCNN'19), Budapest, Hungary, Jul 14-19, 2019.
    52.4% acceptance rate
    
    
    Abstract. This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched with various corresponding correlation structures of the observation noises. Our variational Bayesian SGPR (VBSGPR) models jointly treat both the distributions of the inducing variables and hyperparameters as variational parameters, which enables the decomposability of the variational lower bound that in turn can be exploited for stochastic optimization. Such a stochastic optimization involves iteratively following the stochastic gradient of the variational lower bound to improve its estimates of the optimal variational distributions of the inducing variables and hyperparameters (and hence the predictive distribution) of our VBSGPR models and is guaranteed to achieve asymptotic convergence to them. We show that the stochastic gradient is an unbiased estimator of the exact gradient and can be computed in constant time per iteration, hence achieving scalability to big data. We empirically evaluate the performance of our proposed framework on two real-world, massive datasets.
    
    
29. Decentralized High-Dimensional Bayesian Optimization with Factor Graphs.
    Trong Nghia Hoang, Quang Minh Hoang, Ruofei Ouyang & Kian Hsiang Low.
    In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI-18), pages 3231-3238, New Orleans, LA, Feb 2-8, 2018.
    24.55% acceptance rate
    
    
    Abstract. This paper presents a novel decentralized high-dimensional Bayesian optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms, can exploit the interdependent effects of various input components on the output of the unknown objective function f for boosting the BO performance and still preserve scalability in the number of input dimensions without requiring prior knowledge or the existence of a low (effective) dimension of the input space. To realize this, we propose a sparse yet rich factor graph representation of f to be exploited for designing an acquisition function that can be similarly represented by a sparse factor graph and hence be efficiently optimized in a decentralized manner using distributed message passing. Despite richly characterizing the interdependent effects of the input components on the output of f with a factor graph, DEC-HBO can still guarantee (asymptotic) no-regret performance. Empirical evaluation on synthetic and real-world experiments shows that DEC-HBO outperforms the state-of-the-art HBO algorithms.
    
    
30. Gaussian Process Decentralized Data Fusion Meets Transfer Learning in Large-Scale Distributed Cooperative Perception.
    Ruofei Ouyang & Kian Hsiang Low.
    In Proceedings of the 32nd AAAI Conference on Artificial Intelligence (AAAI-18), pages 3876-3883, New Orleans, LA, Feb 2-8, 2018.
    24.55% acceptance rate
    
    
    Abstract. This paper presents novel Gaussian process decentralized data fusion algorithms exploiting the notion of agent-centric support sets for distributed cooperative perception of large-scale environmental phenomena. To overcome the limitations of scale in existing works, our proposed algorithms allow every mobile sensing agent to choose a different support set and dynamically switch to another during execution for encapsulating its own data into a local summary that, perhaps surprisingly, can still be assimilated with the other agents' local summaries (i.e., based on their current choices of support sets) into a globally consistent summary to be used for predicting the phenomenon. To achieve this, we propose a novel transfer learning mechanism for a team of agents capable of sharing and transferring information encapsulated in a summary based on a support set to that utilizing a different support set with some loss that can be theoretically bounded and analyzed. To alleviate the issue of information loss accumulating over multiple instances of transfer learning, we propose a new information sharing mechanism to be incorporated into our algorithms in order to achieve memory-efficient lazy transfer learning. Empirical evaluation on real-world datasets show that our algorithms outperform the state-of-the-art methods.
    
    
31. Artificial Intelligence Research in Singapore: Assisting the Development of a Smart Nation.
    Pradeep Varakantham, Bo An, Bryan Low & Jie Zhang.
    In AI Magazine, volume 38, issue 3, pages 102-105, Fall 2017.
    
    
    
    Abstract. Artificial Intelligence (AI) research in Singapore is focused on accelerating the country’s development into a Smart Nation. Specifically, AI has been employed extensively in either augmenting the intelligence of humans or in developing automated methods and systems to improve quality of life in Singapore.
    
    
32. Distributed Batch Gaussian Process Optimization.
    Erik Daxberger & Kian Hsiang Low.
    In Proceedings of the 34th International Conference on Machine Learning (ICML-17), pages 951-960, Sydney, Australia, Aug 6-11, 2017.
    25.9% acceptance rate
    
    
    Abstract. This paper presents a novel distributed batch Gaussian process upper confidence bound (DB-GP-UCB) algorithm for performing batch Bayesian optimization (BO) of highly complex, costly-to-evaluate black-box objective functions. In contrast to existing batch BO algorithms, DB-GP-UCB can jointly optimize a batch of inputs (as opposed to selecting the inputs of a batch one at a time) while still preserving scalability in the batch size. To realize this, we generalize GP-UCB to a new batch variant amenable to a Markov approximation, which can then be naturally formulated as a multi-agent distributed constraint optimization problem in order to fully exploit the efficiency of its state-of-the-art solvers for achieving linear time in the batch size. Our DB-GP-UCB algorithm offers practitioners the flexibility to trade off between the approximation quality and time efficiency by varying the Markov order. We provide a theoretical guarantee for the convergence rate of DB-GP-UCB via bounds on its cumulative regret. Empirical evaluation on synthetic benchmark objective functions and a real-world optimization problem shows that DB-GP-UCB outperforms the state-of-the-art batch BO algorithms.
    
    
33. A Generalized Stochastic Variational Bayesian Hyperparameter Learning Framework for Sparse Spectrum Gaussian Process Regression.
    Quang Minh Hoang, Trong Nghia Hoang & Kian Hsiang Low.
    In Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI-17), pages 2007-2014, San Francisco, CA, Feb 4-9, 2017.
    24.6% acceptance rate (oral presentation)
    
    
    Abstract. While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that exploit the sparse spectral representation of a GP kernel. This paper presents such an effort to advance the state of the art of sparse spectrum GP models to achieve competitive predictive performance for massive datasets. Our generalized framework of stochastic variational Bayesian sparse spectrum GP (sVBSSGP) models addresses their shortcomings by adopting a Bayesian treatment of the spectral frequencies to avoid overfitting, modeling these frequencies jointly in its variational distribution to enable their interaction a posteriori, and exploiting local data for boosting the predictive performance. However, such structural improvements result in a variational lower bound that is intractable to be optimized. To resolve this, we exploit a variational parameterization trick to make it amenable to stochastic optimization. Interestingly, the resulting stochastic gradient has a linearly decomposable structure that can be exploited to refine our stochastic optimization method to incur constant time per iteration while preserving its property of being an unbiased estimator of the exact gradient of the variational lower bound. Empirical evaluation on real-world datasets shows that sVBSSGP outperforms state-of-the-art stochastic implementations of sparse GP models.
    
    
34. A Distributed Variational Inference Framework for Unifying Parallel Sparse Gaussian Process Regression Models.
    Trong Nghia Hoang, Quang Minh Hoang & Kian Hsiang Low.
    In Proceedings of the 33rd International Conference on Machine Learning (ICML-16), pages 382-391, New York City, NY, Jun 19-24, 2016.
    24.3% acceptance rate
    
    
    Abstract. This paper presents a novel distributed variational inference framework that unifies many parallel sparse Gaussian process regression (SGPR) models for scalable hyperparameter learning with big data. To achieve this, our framework exploits a structure of correlated noise process model that represents the observation noises as a finite realization of a high-order Gaussian Markov random process. By varying the Markov order and covariance function for the noise process model, different variational SGPR models result. This consequently allows the correlation structure of the noise process model to be characterized for which a particular variational SGPR model is optimal. We empirically evaluate the predictive performance and scalability of the distributed variational SGPR models unified by our framework on two real-world datasets.
    
    
35. Near-Optimal Active Learning of Multi-Output Gaussian Processes.
    Yehong Zhang, Trong Nghia Hoang, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI-16), pages 2351-2357, Phoenix, AZ, Feb 12-17, 2016.
    25.75% acceptance rate
    
    
    Abstract. This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learning criterion. Then, we exploit a relaxed form of sub-modularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for active learning of MOGP and single-output GP models.
    
    
36. Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond.
    Chun Kai Ling, Kian Hsiang Low & Patrick Jaillet.
    In Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI-16), pages 1860-1866, Phoenix, AZ, Feb 12-17, 2016.
    25.75% acceptance rate
    
    
    Abstract. This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive ϵ-optimal GPP (ϵ-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of ϵ-GPP with performance guarantee. We empirically demonstrate the effectiveness of our ϵ-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.
    
    
37. DrMAD: Distilling Reverse-Mode Automatic Differentiation for Optimizing Hyperparameters of Deep Neural Networks.
    Jie Fu, Hongyin Luo, Jiashi Feng, Kian Hsiang Low & Tat-Seng Chua.
    In Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI-16), pages 1469-1475, New York City, NY, Jul 9-15, 2016.
    <25% acceptance rate
    
    
    Abstract. The performance of deep neural networks is well-known to be sensitive to the setting of their hyperparameters. Recent advances in reverse-mode automatic differentiation allow for optimizing hyperparameters with gradients. The standard way of computing these gradients involves a forward and backward pass of computations. However, the backward pass usually needs to consume unaffordable memory to store all the intermediate variables to exactly reverse the forward training procedure. In this work, we propose a simple but effective method, DrMAD, to distill the knowledge of the forward pass into a shortcut path, through which we approximately reverse the training trajectory. Experiments on two image benchmark datasets show that DrMAD is at least 45 times faster and consumes 100 times less memory compared to state-of-the-art methods for optimizing hyperparameters with minimal compromise to its effectiveness. To the best of our knowledge, DrMAD is the first research attempt to make it practical to automatically tune thousands of hyperparameters of deep neural networks.
    
    
38. Multi-Agent Continuous Transportation with Online Balanced Partitioning.
    Chao Wang, Somchaya Liemhetcharat & Kian Hsiang Low.
    In Proceedings of the 15th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-16), pages 1303-1304, Singapore, May 9-13, 2016.
    
    
    
    Abstract. We introduce the concept of continuous transportation task to the context of multi-agent systems. A continuous transportation task is one in which a multi-agent team visits a number of fixed locations, picks up objects, and delivers them to a transportation hub. The goal is to maximize the rate of transportation while the objects are replenished over time. In this extended abstract, we present a hybrid of centralized and distributed approaches that minimize communications in the multi-agent team. We contribute a novel online partitioning-transportation algorithm with information gathering in the multi-agent team.
    
    
39. Concept-based Hybrid Fusion of Multimodal Event Signals.
    Yuhui Wang, Christian von der Weth, Yehong Zhang, Kian Hsiang Low, Vivek Singh & Mohan Kankanhalli.
    In Proceedings of the IEEE International Symposium on Multimedia (ISM'16), pages 14-19, San Jose, CA, Dec 11-13, 2016.
    26.1% acceptance rate
    
    
    Abstract. Recent years have seen a significant increase in the number of sensors and resulting event related sensor data, allowing for a better monitoring and understanding of real-world events and situations. Event-related data come from not only physical sensors (e.g., CCTV cameras, webcams) but also social or microblogging platforms (e.g., Twitter). Given the wide-spread availability of sensors, we observe that sensors of different modalities often independently observe the same events. We argue that fusing multimodal data about an event can be helpful for more accurate detection, localization and detailed description of events of interest. However, multimodal data often include noisy observations, varying information densities and heterogeneous representations, which makes the fusion a challenging task. In this paper, we propose a hybrid fusion approach that takes the spatial and semantic characteristics of sensor signals about events into account. For this, we first adopt the concept of an image-based representation that expresses the situation of particular visual concepts (e.g., "crowdedness", "people marching") called Cmage for both physical and social sensor data. Based on this Cmage representation, we model sparse sensor information using a Gaussian process, fuses multimodal event signals with a Bayesian approach, and incorporates spatial relations between the sensor and social observations. We demonstrate the effectiveness of our approach as a proof-of-concept over real-world data. Our early results show that the proposed approach can reliably reduce the sensor-related noise, localize event place, improve event detection reliability, and add semantic context so that the fused data provide a better picture of the observed events or situations.
    
    
40. Inverse Reinforcement Learning with Locally Consistent Reward Functions.
    Quoc Phong Nguyen, Kian Hsiang Low & Patrick Jaillet.
    In C. Cortes, N. D. Lawrence, D. D. Lee, M. Sugiyama, R. Garnett, editors, Advances in Neural Information Processing Systems 28: 29th Annual Conference on Neural Information Processing Systems (NeurIPS'15), pages 1747-1755, Curran Associates, Inc., Montreal, Canada, Dec 7-12, 2015.
    21.9% acceptance rate
    
    
    Abstract. Existing inverse reinforcement learning (IRL) algorithms have assumed each expert's demonstrated trajectory to be produced by only a single reward function. This paper presents a novel generalization of the IRL problem that allows each trajectory to be generated by multiple locally consistent reward functions, hence catering to more realistic and complex experts' behaviors. Solving our generalized IRL problem thus involves not only learning these reward functions but also the stochastic transitions between them at any state (including unvisited states). By representing our IRL problem with a probabilistic graphical model, an expectation-maximization (EM) algorithm can be devised to iteratively learn the reward functions and stochastic transitions between them in order to jointly improve the likelihood of the expert's demonstrated trajectories. As a result, the most likely partition of a trajectory into segments that are generated from different locally consistent reward functions selected by EM can be derived. Empirical evaluation on synthetic and real-world datasets shows that our IRL algorithm outperforms the state-of-the-art EM clustering with maximum likelihood IRL, which is, interestingly, a reduced variant of our approach.
    
    
41. Gaussian Process Decentralized Data Fusion and Active Sensing for Spatiotemporal Traffic Modeling and Prediction in Mobility-on-Demand Systems.
    Jie Chen, Kian Hsiang Low, Patrick Jaillet & Yujian Yao.
    In IEEE Transactions on Automation Science and Engineering (Special Issue on Networked Cooperative Autonomous Systems), volume 12, issue 3, pages 901-921, Jul 2015.
    Extended version of our UAI-12 and RSS-13 papers
    
    
    Abstract. Mobility-on-demand (MoD) systems have recently emerged as a promising paradigm of one-way vehicle sharing for sustainable personal urban mobility in densely populated cities. We assume the capability of a MoD system to be enhanced by deploying robotic shared vehicles that can autonomously cruise the streets to be hailed by users. A key challenge of the MoD system is that of real-time, fine-grained mobility demand and traffic flow sensing and prediction. This paper presents novel Gaussian process (GP) decentralized data fusion and active sensing algorithms for real-time, fine-grained traffic modeling and prediction with a fleet of MoD vehicles. The predictive performance of our decentralized data fusion algorithms are theoretically guaranteed to be equivalent to that of sophisticated centralized sparse GP approximations. We derive consensus filtering variants requiring only local communication between neighboring vehicles. We theoretically guarantee the performance of our decentralized active sensing algorithms. When they are used to gather informative data for mobility demand prediction, they can achieve a dual effect of fleet rebalancing to service mobility demands. Empirical evaluation on real-world datasets shows that our algorithms are significantly more time-efficient and scalable in the size of data and fleet while achieving predictive performance comparable to that of state-of-the-art algorithms.
    
    
42. A Unifying Framework of Anytime Sparse Gaussian Process Regression Models with Stochastic Variational Inference for Big Data.
    Trong Nghia Hoang, Quang Minh Hoang & Kian Hsiang Low.
    In Proceedings of the 32nd International Conference on Machine Learning (ICML-15), pages 569-578, Lille, France, Jul 6-11, 2015.
    26.0% acceptance rate
    
    
    Abstract. This paper presents a novel unifying framework of anytime sparse Gaussian process regression (SGPR) models that can produce good predictive performance fast and improve their predictive performance over time. Our proposed unifying framework reverses the variational inference procedure to theoretically construct a non-trivial, concave functional that is maximized at the predictive distribution of any SGPR model of our choice. As a result, a stochastic natural gradient ascent method can be derived that involves iteratively following the stochastic natural gradient of the functional to improve its estimate of the predictive distribution of the chosen SGPR model and is guaranteed to achieve asymptotic convergence to it. Interestingly, we show that if the predictive distribution of the chosen SGPR model satisfies certain decomposability conditions, then the stochastic natural gradient is an unbiased estimator of the exact natural gradient and can be computed in constant time (i.e., independent of data size) at each iteration. We empirically evaluate the trade-off between the predictive performance vs. time efficiency of the anytime SGPR models on two real-world million-sized datasets.
    
    
43. Parallel Gaussian Process Regression for Big Data: Low-Rank Representation Meets Markov Approximation.
    Kian Hsiang Low, Jiangbo Yu, Jie Chen & Patrick Jaillet.
    In Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI-15), pages 2821-2827, Austin, TX, Jan 25-29, 2015.
    26.67% acceptance rate
    
    
    Abstract. The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complementing a low-rank approximate representation of the full-rank GP based on a support set of inputs with a Markov approximation of the resulting residual process; the latter approximation is guaranteed to be closest in the Kullback-Leibler distance criterion subject to some constraint and is considerably more refined than that of existing sparse GP models utilizing low-rank representations due to its more relaxed conditional independence assumption (especially with larger data). As a result, our LMA method can trade off between the size of the support set and the order of the Markov property to (a) incur lower computational cost than such sparse GP models while achieving predictive performance comparable to them and (b) accurately represent features/patterns of any scale. Interestingly, varying the Markov order produces a spectrum of LMAs with PIC approximation and full-rank GP at the two extremes. An advantage of our LMA method is that it is amenable to parallelization on multiple machines/cores, thereby gaining greater scalability. Empirical evaluation on three real-world datasets in clusters of up to 32 computing nodes shows that our centralized and parallel LMA methods are significantly more time-efficient and scalable than state-of-the-art sparse and full-rank GP regression methods while achieving comparable predictive performances.
    
    
44. Recent Advances in Scaling up Gaussian Process Predictive Models for Large Spatiotemporal Data.
    Kian Hsiang Low, Jie Chen, Trong Nghia Hoang, Nuo Xu & Patrick Jaillet.
    In S. Ravela, A. Sandu, editors, Dynamic Data-Driven Environmental Systems Science - First International Conference, DyDESS'14, LNCS 8964, pages 167-181, Springer International Publishing, MIT, Cambridge, MA, Nov 5-7, 2014.
    Oral presentation
    
    
    Abstract. The expressive power of Gaussian process (GP) models comes at a cost of poor scalability in the size of the data. To improve their scalability, this paper presents an overview of our recent progress in scaling up GP models for large spatiotemporally correlated data through parallelization on clusters of machines, online learning, and nonmyopic active sensing/learning.
    
    
45. Multi-Agent Ad Hoc Team Partitioning by Observing and Modeling Single-Agent Performance.
    Etkin Baris Ozgul, Somchaya Liemhetcharat & Kian Hsiang Low.
    In Proceedings of the Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC'14), pages 1-7, Siem Reap, city of Angkor Wat, Cambodia, Dec 9-12, 2014.
    
    
    
    Abstract. Multi-agent research has focused on finding the optimal team for a task. Many approaches assume that the performance of the agents are known a priori. We are interested in ad hoc teams, where the agents' algorithms and performance are initially unknown. We focus on the task of modeling the performance of single agents through observation in training environments, and using the learned models to partition a new environment for a multi-agent team. The goal is to minimize the number of agents used, while maintaining a performance threshold of the multi-agent team. We contribute a novel model to learn the agent's performance through observations, and a partitioning algorithm that minimizes the team size. We evaluate our algorithms in simulation, and show the efficacy of our learn model and partitioning algorithm.
    
    
46. Scalable Decision-Theoretic Coordination and Control for Real-time Active Multi-Camera Surveillance.
    Prabhu Natarajan, Trong Nghia Hoang, Yongkang Wong, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 8th ACM/IEEE International Conference on Distributed Smart Cameras (ICDSC'14) (Invited Paper to Special Session on Smart Cameras for Smart Environments), pages 115-120, Venezia, Italy, Nov 4-7, 2014.
    
    
    
    Abstract. This paper presents an overview of our novel decision-theoretic multi-agent approach for controlling and coordinating multiple active cameras in surveillance. In this approach, a surveillance task is modeled as a stochastic optimization problem, where the active cameras are controlled and coordinated to achieve the desired surveillance goal in presence of uncertainties. We enumerate the practical issues in active camera surveillance and discuss how these issues are addressed in our decision-theoretic approach. We focus on two novel surveillance tasks: maximize the number of targets observed in active cameras with guaranteed image resolution and to improve the fairness in observation of multiple targets. We discuss the overview of our novel decision-theoretic frameworks: Markov decision process and partially observable Markov decision process frameworks for coordinating active cameras in uncertain and partially occluded environments.
    
    
47. Active Learning is Planning: Nonmyopic ϵ-Bayes-Optimal Active Learning of Gaussian Processes.
    Trong Nghia Hoang, Kian Hsiang Low, Patrick Jaillet and Mohan Kankanhalli.
    In T. Calders, F. Esposito, E. Hüllermeier, R. Meo, editors, Machine Learning and Knowledge Discovery in Databases - European Conference, ECML/PKDD-14 Nectar (New Scientific and Technical Advances in Research) Track, Part III, LNCS 8726, pages 494-498, Springer Berlin Heidelberg, Nancy, France, Sep 15-19, 2014.
    
    
    
    Abstract. A fundamental issue in active learning of Gaussian processes is that of the exploration-exploitation trade-off. This paper presents a novel nonmyopic ϵ-Bayes-optimal active learning (ϵ-BAL) approach that jointly optimizes the trade-off. In contrast, existing works have primarily developed greedy algorithms or performed exploration and exploitation separately. To perform active learning in real time, we then propose an anytime algorithm based on ϵ-BAL with performance guarantee and empirically demonstrate using a real-world dataset that, with limited budget, it outperforms the state-of-the-art algorithms.
    
    
48. Generalized Online Sparse Gaussian Processes with Application to Persistent Mobile Robot Localization.
    Kian Hsiang Low, Nuo Xu, Jie Chen, Keng Kiat Lim & Etkin Baris Ozgul.
    In T. Calders, F. Esposito, E. Hüllermeier, R. Meo, editors, Machine Learning and Knowledge Discovery in Databases - European Conference, ECML/PKDD-14 Nectar (New Scientific and Technical Advances in Research) Track, Part III, LNCS 8726, pages 499-503, Springer Berlin Heidelberg, Nancy, France, Sep 15-19, 2014.
    
    
    
    Abstract. This paper presents a novel online sparse Gaussian process (GP) approximation method that is capable of achieving constant time and memory (i.e., independent of the size of the data) per time step. We theoretically guarantee its predictive performance to be equivalent to that of a sophisticated offline sparse GP approximation method. We empirically demonstrate the practical feasibility of using our online sparse GP approximation method through a real-world persistent mobile robot localization experiment.
    
    
49. No One is Left "Unwatched": Fairness in Observation of Crowds of Mobile Targets in Active Camera Surveillance.
    Prabhu Natarajan, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 21st European Conference on Artificial Intelligence (ECAI-14), including Prestigious Applications of Intelligent Systems (PAIS-14), pages 1155-1160, Prague, Czech Republic, Aug 18-22, 2014.
    
    
    
    Abstract. Central to the problem of active multi-camera surveillance is the fundamental issue of fairness in the observation of crowds of targets such that no target is "starved" of observation by the cameras for a long time. This paper presents a principled decision-theoretic multi-camera coordination and control (MC²) algorithm called fair-MC² that can coordinate and control the active cameras to achieve max-min fairness in the observation of crowds of targets moving stochastically. Our fair-MC² algorithm is novel in demonstrating how (a) the uncertainty in the locations, directions, speeds, and observation times of the targets arising from the stochasticity of their motion can be modeled probabilistically, (b) the notion of fairness in observing targets can be formally realized in the domain of multi-camera surveillance for the first time by exploiting the max-min fairness metric to formalize our surveillance objective, that is, to maximize the expected minimum observation time over all targets while guaranteeing a predefined image resolution of observing them, and (c) a structural assumption in the state transition dynamics of a surveillance environment can be exploited to improve its scalability to linear time in the number of targets to be observed during surveillance. Empirical evaluation through extensive simulations in realistic surveillance environments shows that fair-MC² outperforms the state-of-the-art and baseline MC² algorithms. We have also demonstrated the feasibility of deploying our fair-MC² algorithm on real AXIS 214 PTZ cameras.
    
    
50. GP-Localize: Persistent Mobile Robot Localization using Online Sparse Gaussian Process Observation Model.
    Nuo Xu, Kian Hsiang Low, Jie Chen, Keng Kiat Lim & Etkin Baris Ozgul.
    In Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI-14), pages 2585-2592, Quebec City, Canada, Jul 27-31, 2014.
    16.6% acceptance rate (oral presentation)
    Also appeared in RSS-14 Workshop on Non-Parametric Learning in Robotics, Berkeley, CA, Jul 12, 2014.
    
    
    Abstract. Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurements taken during a robot's exploration (instead of relying on prior training data) for efficiently and scalably learning the GP observation model online through our proposed novel online sparse GP. As a result, GP-Localize is capable of achieving constant time and memory (i.e., independent of the size of the data) per filtering step, which demonstrates the practical feasibility of using GPs for persistent robot localization and autonomy. Empirical evaluation via simulated experiments with real-world datasets and a real robot experiment shows that GP-Localize outperforms existing GP localization algorithms.
    
    
51. Nonmyopic ϵ-Bayes-Optimal Active Learning of Gaussian Processes.
    Trong Nghia Hoang, Kian Hsiang Low, Patrick Jaillet and Mohan Kankanhalli.
    In Proceedings of the 31st International Conference on Machine Learning (ICML-14), pages 739-747, Beijing, China, Jun 21-26, 2014.
    22.4% acceptance rate (cycle 2)
    Also appeared in RSS-14 Workshop on Non-Parametric Learning in Robotics, Berkeley, CA, Jul 12, 2014.
    
    
    Abstract. A fundamental issue in active learning of Gaussian processes is that of the exploration-exploitation trade-off. This paper presents a novel nonmyopic ϵ-Bayes-optimal active learning (ϵ-BAL) approach that jointly and naturally optimizes the trade-off. In contrast, existing works have primarily developed myopic/greedy algorithms or performed exploration and exploitation separately. To perform active learning in real time, we then propose an anytime algorithm based on ϵ-BAL with performance guarantee and empirically demonstrate using synthetic and real-world datasets that, with limited budget, it outperforms the state-of-the-art algorithms.
    
    
52. Multi-Robot Active Sensing of Non-Stationary Gaussian Process-Based Environmental Phenomena.
    Ruofei Ouyang, Kian Hsiang Low, Jie Chen & Patrick Jaillet.
    In Proceedings of the 13th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-14), pages 573-580, Paris, France, May 5-9, 2014.
    23.8% acceptance rate
    Also appeared in RSS-14 Workshop on Non-Parametric Learning in Robotics, Berkeley, CA, Jul 12, 2014.
    
    
    Abstract. A key challenge of environmental sensing and monitoring is that of sensing, modeling, and predicting large-scale, spatially correlated environmental phenomena, especially when they are unknown and non-stationary. This paper presents a decentralized multi-robot active sensing (DEC-MAS) algorithm that can efficiently coordinate the exploration of multiple robots to gather the most informative observations for predicting an unknown, non-stationary phenomenon. By modeling the phenomenon using a Dirichlet process mixture of Gaussian processes (DPM-GPs), our work here is novel in demonstrating how DPM-GPs and its structural properties can be exploited to (a) formalize an active sensing criterion that trades off between gathering the most informative observations for estimating the unknown, non-stationary spatial correlation structure vs. that for predicting the phenomenon given the current, imprecise estimate of the correlation structure, and (b) support efficient decentralized coordination. We also provide a theoretical performance guarantee for DEC-MAS and analyze its time complexity. We empirically demonstrate using two real-world datasets that DEC-MAS outperforms state-of-the-art MAS algorithms.
    
    
53. Decision-Theoretic Approach to Maximizing Fairness in Multi-Target Observation in Multi-Camera Surveillance.
    Prabhu Natarajan, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 13th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-14), pages 1521-1522, Paris, France, May 5-9, 2014.
    
    
    
    Abstract. Central to the problem of active multi-camera surveillance is the fundamental issue of fairness in the observation of multiple targets such that no target is left unobserved by the cameras for a long time. To address this important issue, we propose a novel principled decision-theoretic approach to control and coordinate multiple active cameras to achieve fairness in the observation of multiple moving targets.
    
    
54. Interactive POMDP Lite: Towards Practical Planning to Predict and Exploit Intentions for Interacting with Self-Interested Agents.
    Trong Nghia Hoang & Kian Hsiang Low.
    In Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI-13), pages 2298-2305, Beijing, China, Aug 3-9, 2013.
    13.2% acceptance rate (oral presentation)
    
    
    Abstract. A key challenge in non-cooperative multi-agent systems is that of developing efficient planning algorithms for intelligent agents to interact and perform effectively among boundedly rational, self-interested agents (e.g., humans). The practicality of existing works addressing this challenge is being undermined due to either the restrictive assumptions of the other agents' behavior, the failure in accounting for their rationality, or the prohibitively expensive cost of modeling and predicting their intentions. To boost the practicality of research in this field, we investigate how intention prediction can be efficiently exploited and made practical in planning, thereby leading to efficient intention-aware planning frameworks capable of predicting the intentions of other agents and acting optimally with respect to their predicted intentions. We show that the performance losses incurred by the resulting planning policies are linearly bounded by the error of intention prediction. Empirical evaluations through a series of stochastic games demonstrate that our policies can achieve better and more robust performance than the state-of-the-art algorithms.
    
    
55. A General Framework for Interacting Bayes-Optimally with Self-Interested Agents using Arbitrary Parametric Model and Model Prior.
    Trong Nghia Hoang & Kian Hsiang Low.
    In Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI-13), pages 1394-1400, Beijing, China, Aug 3-9, 2013.
    28.0% acceptance rate
    
    
    Abstract. Recent advances in Bayesian reinforcement learning (BRL) have shown that Bayes-optimality is theoretically achievable by modeling the environment's latent dynamics using Flat-Dirichlet-Multinomial (FDM) prior. In self-interested multi-agent environments, the transition dynamics are mainly controlled by the other agent's stochastic behavior for which FDM's independence and modeling assumptions do not hold. As a result, FDM does not allow the other agent's behavior to be generalized across different states nor specified using prior domain knowledge. To overcome these practical limitations of FDM, we propose a generalization of BRL to integrate the general class of parametric models and model priors, thus allowing practitioners' domain knowledge to be exploited to produce a fine-grained and compact representation of the other agent's behavior. Empirical evaluation shows that our approach outperforms existing multi-agent reinforcement learning algorithms.
    
    
56. Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations.
    Jie Chen, Nannan Cao, Kian Hsiang Low, Ruofei Ouyang, Colin Keng-Yan Tan & Patrick Jaillet.
    In Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence (UAI-13), pages 152-161, Bellevue, WA, Jul 11-15, 2013.
    31.3% acceptance rate
    
    
    Abstract. Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank covariance matrix approximations for distributing the computational load among parallel machines to achieve time efficiency and scalability. We theoretically guarantee the predictive performances of our proposed parallel GPs to be equivalent to that of some centralized approximate GP regression methods: The computation of their centralized counterparts can be distributed among parallel machines, hence achieving greater time efficiency and scalability. We analytically compare the properties of our parallel GPs such as time, space, and communication complexity. Empirical evaluation on two real-world datasets in a cluster of 20 computing nodes shows that our parallel GPs are significantly more time-efficient and scalable than their centralized counterparts and exact/full GP while achieving predictive performances comparable to full GP.
    
    
57. Gaussian Process-Based Decentralized Data Fusion and Active Sensing for Mobility-on-Demand System.
    Jie Chen, Kian Hsiang Low & Colin Keng-Yan Tan.
    In Proceedings of the Robotics: Science and Systems Conference (RSS-13), Berlin, Germany, Jun 24-28, 2013.
    30.1% acceptance rate
    
    
    Abstract. Mobility-on-demand (MoD) systems have recently emerged as a promising paradigm of one-way vehicle sharing for sustainable personal urban mobility in densely populated cities. In this paper, we enhance the capability of a MoD system by deploying robotic shared vehicles that can autonomously cruise the streets to be hailed by users. A key challenge to managing the MoD system effectively is that of real-time, fine-grained mobility demand sensing and prediction. This paper presents a novel decentralized data fusion and active sensing algorithm for real-time, fine-grained mobility demand sensing and prediction with a fleet of autonomous robotic vehicles in a MoD system. Our Gaussian process (GP)-based decentralized data fusion algorithm can achieve a fine balance between predictive power and time efficiency. We theoretically guarantee its predictive performance to be equivalent to that of a sophisticated centralized sparse approximation for the GP model: The computation of such a sparse approximate GP model can thus be distributed among the MoD vehicles, hence achieving efficient and scalable demand prediction. Though our decentralized active sensing strategy is devised to gather the most informative demand data for demand prediction, it can achieve a dual effect of fleet rebalancing to service the mobility demands. Empirical evaluation on real-world mobility demand data shows that our proposed algorithm can achieve a better balance between predictive accuracy and time efficiency than state-of-the-art algorithms.
    
    
58. Multi-Robot Informative Path Planning for Active Sensing of Environmental Phenomena: A Tale of Two Algorithms.
    Nannan Cao, Kian Hsiang Low & John M. Dolan.
    In Proceedings of the 12th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-13), pages 7-14, Saint Paul, MN, May 6-10, 2013.
    22.9% acceptance rate
    
    
    Abstract. A key problem of robotic environmental sensing and monitoring is that of active sensing: How can a team of robots plan the most informative observation paths to minimize the uncertainty in modeling and predicting an environmental phenomenon? This paper presents two principled approaches to efficient information-theoretic path planning based on entropy and mutual information criteria for in situ active sensing of an important broad class of widely-occurring environmental phenomena called anisotropic fields. Our proposed algorithms are novel in addressing a trade-off between active sensing performance and time efficiency. An important practical consequence is that our algorithms can exploit the spatial correlation structure of Gaussian process-based anisotropic fields to improve time efficiency while preserving near-optimal active sensing performance. We analyze the time complexity of our algorithms and prove analytically that they scale better than state-of-the-art algorithms with increasing planning horizon length. We provide theoretical guarantees on the active sensing performance of our algorithms for a class of exploration tasks called transect sampling, which, in particular, can be improved with longer planning time and/or lower spatial correlation along the transect. Empirical evaluation on real-world anisotropic field data shows that our algorithms can perform better or at least as well as the state-of-the-art algorithms while often incurring a few orders of magnitude less computational time, even when the field conditions are less favorable.
    
    
59. Adaptive Sampling of Time Series with Application to Remote Exploration.
    David R. Thompson, Nathalie Cabrol, Michael Furlong, Craig Hardgrove, Kian Hsiang Low, Jeffrey Moersch & David Wettergreen.
    In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'13), pages 3463-3468, Karlsruhe, Germany, May 6-10, 2013.
    
    
    
    Abstract. We address the problem of adaptive information-optimal data collection in time series. Here a remote sensor or explorer agent throttles its sampling rate in order to track anomalous events while obeying constraints on time and power. This problem is challenging because the agent has limited visibility - all collected datapoints lie in the past, but its resource allocation decisions require predicting far into the future. Our solution is to continually fit a Gaussian process model to the latest data and optimize the sampling plan on line to maximize information gain. We compare the performance characteristics of stationary and nonstationary Gaussian process models. We also describe an application based on geologic analysis during planetary rover exploration. Here adaptive sampling can improve coverage of localized anomalies and potentially benefit mission science yield of long autonomous traverses.
    
    
60. Decentralized Data Fusion and Active Sensing with Mobile Sensors for Modeling and Predicting Spatiotemporal Traffic Phenomena.
    Jie Chen, Kian Hsiang Low, Colin Keng-Yan Tan, Ali Oran, Patrick Jaillet, John M. Dolan & Gaurav S. Sukhatme.
    In Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence (UAI-12), pages 163-173, Catalina Island, CA, Aug 15-17, 2012.
    31.6% acceptance rate
    Also appeared in AAMAS-12 Workshop on Agents in Traffic and Transportation (ATT-12), Valencia, Spain, June 4-8, 2012.
    
    
    Abstract. The problem of modeling and predicting spatiotemporal traffic phenomena over an urban road network is important to many traffic applications such as detecting and forecasting congestion hotspots. This paper presents a decentralized data fusion and active sensing (D2FAS) algorithm for mobile sensors to actively explore the road network to gather and assimilate the most informative data for predicting the traffic phenomenon. We analyze the time and communication complexity of D2FAS and demonstrate that it can scale well with a large number of observations and sensors. We provide a theoretical guarantee on its predictive performance to be equivalent to that of a sophisticated centralized sparse approximation for the Gaussian process (GP) model: The computation of such a sparse approximate GP model can thus be parallelized and distributed among the mobile sensors (in a Google-like MapReduce paradigm), thereby achieving efficient and scalable prediction. We also theoretically guarantee its active sensing performance that improves under various practical environmental conditions. Empirical evaluation on real-world urban road network data shows that our D2FAS algorithm is significantly more time-efficient and scalable than state-of-the-art centralized algorithms while achieving comparable predictive performance.
    
    
61. Hierarchical Bayesian Nonparametric Approach to Modeling and Learning the Wisdom of Crowds of Urban Traffic Route Planning Agents.
    Jiangbo Yu, Kian Hsiang Low, Ali Oran & Patrick Jaillet.
    In Proceedings of the IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT'12) (Invited Paper to Special Session on Large-Scale Application-Focused Multi-Agent Systems), pages 478-485, Macau, Dec 4-7, 2012.
    
    
    
    Abstract. Route prediction is important to analyzing and understanding the route patterns and behavior of traffic crowds. Its objective is to predict the most likely or "popular" route of road segments from a given point in a road network. This paper presents a hierarchical Bayesian non-parametric approach to efficient and scalable route prediction that can harness the wisdom of crowds of route planning agents by aggregating their sequential routes of possibly varying lengths and origin-destination pairs. In particular, our approach has the advantages of (a) not requiring a Markov assumption to be imposed and (b) generalizing well with sparse data, thus resulting in significantly improved prediction accuracy, as demonstrated empirically using real-world taxi route data. We also show two practical applications of our route prediction algorithm: predictive taxi ranking and route recommendation.
    
    
62. Decision-Theoretic Coordination and Control for Active Multi-Camera Surveillance in Uncertain, Partially Observable Environments.
    Prabhu Natarajan, Trong Nghia Hoang, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 6th ACM/IEEE International Conference on Distributed Smart Cameras (ICDSC'12), pages 1-6, Hong Kong, Oct 30 - Nov 2, 2012.
    
    
    
    Abstract. A central problem of surveillance is to monitor multiple targets moving in a large-scale, obstacle-ridden environment with occlusions. This paper presents a novel principled Partially Observable Markov Decision Process-based approach to coordinating and controlling a network of active cameras for tracking and observing multiple mobile targets at high resolution in such surveillance environments. Our proposed approach is capable of (a) maintaining a belief over the targets' states (i.e., locations, directions, and velocities) to track them, even when they may not be observed directly by the cameras at all times, (b) coordinating the cameras' actions to simultaneously improve the belief over the targets' states and maximize the expected number of targets observed with a guaranteed resolution, and (c) exploiting the inherent structure of our surveillance problem to improve its scalability (i.e., linear time) in the number of targets to be observed. Quantitative comparisons with state-of-the-art multi-camera coordination and control techniques show that our approach can achieve higher surveillance quality in real time. The practical feasibility of our approach is also demonstrated using real AXIS 214 PTZ cameras.
    
    
63. Decentralized Active Robotic Exploration and Mapping for Probabilistic Field Classification in Environmental Sensing.
    Kian Hsiang Low, Jie Chen, John M. Dolan, Steve Chien & David R. Thompson.
    In Proceedings of the 11th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-12), pages 105-112, Valencia, Spain, June 4-8, 2012.
    20.4% acceptance rate
    Also appeared in IROS'11 Workshop on Robotics for Environmental Monitoring (WREM-11), San Francisco, CA, Sep 30, 2011.
    
    
    Abstract. A central problem in environmental sensing and monitoring is to classify/label the hotspots in a large-scale environmental field. This paper presents a novel decentralized active robotic exploration (DARE) strategy for probabilistic classification/labeling of hotspots in a Gaussian process (GP)-based field. In contrast to existing state-of-the-art exploration strategies for learning environmental field maps, the time needed to solve the DARE strategy is independent of the map resolution and the number of robots, thus making it practical for in situ, real-time active sampling. Its exploration behavior exhibits an interesting formal trade-off between that of boundary tracking until the hotspot region boundary can be accurately predicted and wide-area coverage to find new boundaries in sparsely sampled areas to be tracked. We provide a theoretical guarantee on the active exploration performance of the DARE strategy: under reasonable conditional independence assumption, we prove that it can optimally achieve two formal cost-minimizing exploration objectives based on the misclassification and entropy criteria. Importantly, this result implies that the uncertainty of labeling the hotspots in a GP-based field is greatest at or close to the hotspot region boundaries. Empirical evaluation on real-world plankton density and temperature field data shows that, subject to limited observations, DARE strategy can achieve more superior classification of hotspots and time efficiency than state-of-the-art active exploration strategies.
    
    
64. Decision-Theoretic Approach to Maximizing Observation of Multiple Targets in Multi-Camera Surveillance.
    Prabhu Natarajan, Trong Nghia Hoang, Kian Hsiang Low & Mohan Kankanhalli.
    In Proceedings of the 11th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-12), pages 155-162, Valencia, Spain, June 4-8, 2012.
    20.4% acceptance rate
    
    
    Abstract. This paper presents a novel decision-theoretic approach to control and coordinate multiple active cameras for observing a number of moving targets in a surveillance system. This approach offers the advantages of being able to (a) account for the stochasticity of targets' motion via probabilistic modeling, and (b) address the trade-off between maximizing the expected number of observed targets and the resolution of the observed targets through stochastic optimization. One of the key issues faced by existing approaches in multi-camera surveillance is that of scalability with increasing number of targets. We show how its scalability can be improved by exploiting the problem structure: as proven analytically, our decision-theoretic approach incurs time that is linear in the number of targets to be observed during surveillance. As demonstrated empirically through simulations, our proposed approach can achieve high-quality surveillance of up to 50 targets in real time and its surveillance performance degrades gracefully with increasing number of targets. We also demonstrate our proposed approach with real AXIS 214 PTZ cameras in maximizing the number of Lego robots observed at high resolution over a surveyed rectangular area. The results are promising and clearly show the feasibility of our decision-theoretic approach in controlling and coordinating the active cameras in real surveillance system.
    
    
65. Intention-Aware Planning under Uncertainty for Interacting with Self-Interested, Boundedly Rational Agents.
    Trong Nghia Hoang & Kian Hsiang Low.
    In Proceedings of the 11th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-12), pages 1233-1234, Valencia, Spain, June 4-8, 2012.
    
    
    
    Abstract. A key challenge in non-cooperative multi-agent systems is that of developing efficient planning algorithms for intelligent agents to perform effectively among boundedly rational, self-interested (i.e., non-cooperative) agents (e.g., humans). To address this challenge, we investigate how intention prediction can be efficiently exploited and made practical in planning, thereby leading to efficient intention-aware planning frameworks capable of predicting the intentions of other agents and acting optimally with respect to their predicted intentions.
    
    
66. Active Markov Information-Theoretic Path Planning for Robotic Environmental Sensing.
    Kian Hsiang Low, John M. Dolan & Pradeep Khosla.
    In Proceedings of the 10th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-11), pages 753-760, Taipei, Taiwan, May 2-6, 2011.
    22.1% acceptance rate
    
    
    Abstract. Recent research in multi-robot exploration and mapping has focused on sampling environmental fields, which are typically modeled using the Gaussian process (GP). Existing information-theoretic exploration strategies for learning GP-based environmental field maps adopt the non-Markovian problem structure and consequently scale poorly with the length of history of observations. Hence, it becomes computationally impractical to use these strategies for in situ, real-time active sampling. To ease this computational burden, this paper presents a Markov-based approach to efficient information-theoretic path planning for active sampling of GP-based fields. We analyze the time complexity of solving the Markov-based path planning problem, and demonstrate analytically that it scales better than that of deriving the non-Markovian strategies with increasing length of planning horizon. For a class of exploration tasks called the transect sampling task, we provide theoretical guarantees on the active sampling performance of our Markov-based policy, from which ideal environmental field conditions and sampling task settings can be established to limit its performance degradation due to violation of the Markov assumption. Empirical evaluation on real-world temperature and plankton density field data shows that our Markov-based policy can generally achieve active sampling performance comparable to that of the widely-used non-Markovian greedy policies under less favorable realistic field conditions and task settings while enjoying significant computational gain over them.
    
    
67. Autonomous Personal Vehicle for the First- and Last-Mile Transportation Services.
    Zhuang Jie Chong, Baoxing Qin, Tirthankar Bandyopadhyay, Tichakorn Wongpiromsarn, Edward Samuel Rankin, Marcelo H. Ang, Jr., Emilio Frazzoli, Daniela Rus, David Hsu & Kian Hsiang Low.
    In Proceedings of the 5th IEEE International Conference on Cybernetics and Intelligent Systems and 5th IEEE International Conference on Robotics, Automation and Mechatronics (CIS-RAM'11), pages 253-260, Qingdao, China, Sep 17-19, 2011.
    
    Also appeared in IROS'11 Workshop on Perception and Navigation for Autonomous Vehicles in Human Environment, San Francisco, CA, Sep 30, 2011.
    
    
    Abstract. This paper describes an autonomous vehicle testbed that aims at providing the first- and last- mile transportation services. The vehicle mainly operates in a crowded urban environment whose features can be extracted a priori. To ensure that the system is economically feasible, we take a minimalistic approach and exploit prior knowledge of the environment and the availability of the existing infrastructure such as cellular networks and traffic cameras. We present three main components of the system: pedestrian detection, localization (even in the presence of tall buildings) and navigation. The performance of each component is evaluated. Finally, we describe the role of the existing infrastructural sensors and show the improved performance of the system when they are utilized.
    
    
68. Telesupervised Remote Surface Water Quality Sensing.
    Gregg Podnar, John M. Dolan, Kian Hsiang Low & Alberto Elfes.
    In Proceedings of the IEEE Aerospace Conference, Big Sky, MT, Mar 6-13, 2010.
    
    
    
    Abstract. We present a fleet of autonomous Robot Sensor Boats (RSBs) developed for lake and river fresh water quality assessment and controlled by our Multilevel Autonomy Robot Telesupervision Architecture (MARTA). The RSBs are low cost, highly maneuverable, shallow draft sensor boats, developed as part of the Sensor Web program supported under the Advanced Information Systems Technology program of NASA's Earth Systems Technology Office. They can scan large areas of lakes, and navigate up tributaries to measure water quality near outfalls that larger research vessels cannot reach. The MARTA telesupervision architecture has been applied to a number of domains from multi-platform autonomous wide area planetary mineral prospecting, to multi-platform ocean monitoring. The RSBs are a complementary expansion of a fleet of NOAA/NASA-developed extended-deployment surface autonomous vehicles that enable in-situ study of meteorological factors of the ocean/atmosphere interface, and which have been adapted to investigate harmful algal blooms under this program. The flexibility of the MARTA telesupervision architecture was proven as it supported simultaneous operation of these heterogenous autonomous sensor platforms while geographically widely separated. Results and analysis are presented of multiple tests carried out over three months using a multi-sensor water sonde to assess water quality in a small recreational lake. Inference Grids were used to produce maps representing temperature, pH, and dissolved oxygen. The tests were performed under various water conditions (clear vs. hair algae-laden) and both before and after heavy rains. Data from each RSB was relayed to a data server in our lab in Pittsburgh, Pennsylvania, and made available over the World Wide Web where it was acquired by team members at the Jet Propulsion Laboratory of NASA in Pasadena, California who monitored the boats and their sensor readings in real time, as well as using these data to model the water quality by producing Inference Grid-based maps.
    
    
69. Information-Theoretic Approach to Efficient Adaptive Path Planning for Mobile Robotic Environmental Sensing.
    Kian Hsiang Low, John M. Dolan & Pradeep Khosla.
    In Proceedings of the 19th International Conference on Automated Planning and Scheduling (ICAPS-09), pages 233-240, Thessaloniki, Greece, Sep 19-23, 2009.
    33.9% acceptance rate
    Also appeared in IPSN-09 Workshop on Sensor Networks for Earth and Space Science Applications (ESSA-09), San Francisco, CA, Apr 16, 2009.
    Also orally presented in RSS-09 Workshop on Aquatic Robots and Ocean Sampling, Seattle, WA, Jun 29, 2009.
    
    
    Abstract. Recent research in robot exploration and mapping has focused on sampling environmental hotspot fields. This exploration task is formalized by Low, Dolan, and Khosla (2008) in a sequential decision-theoretic planning under uncertainty framework called MASP. The time complexity of solving MASP approximately depends on the map resolution, which limits its use in large-scale, high-resolution exploration and mapping. To alleviate this computational difficulty, this paper presents an information-theoretic approach to MASP (iMASP) for efficient adaptive path planning; by reformulating the cost-minimizing iMASP as a reward-maximizing problem, its time complexity becomes independent of map resolution and is less sensitive to increasing robot team size as demonstrated both theoretically and empirically. Using the reward-maximizing dual, we derive a novel adaptive variant of maximum entropy sampling, thus improving the induced exploration policy performance. It also allows us to establish theoretical bounds quantifying the performance advantage of optimal adaptive over non-adaptive policies and the performance quality of approximately optimal vs. optimal adaptive policies. We show analytically and empirically the superior performance of iMASP-based policies for sampling the log-Gaussian process to that of policies for the widely-used Gaussian process in mapping the hotspot field. Lastly, we provide sufficient conditions that, when met, guarantee adaptivity has no benefit under an assumed environment model.
    
    
70. Cooperative Aquatic Sensing using the Telesupervised Adaptive Ocean Sensor Fleet.
    John M. Dolan, Gregg W. Podnar, Stephen Stancliff, Kian Hsiang Low, Alberto Elfes, John Higinbotham, Jeffrey C. Hosler, Tiffany A. Moisan & John Moisan.
    In Proceedings of the SPIE Conference on Remote Sensing of the Ocean, Sea Ice, and Large Water Regions, volume 7473, Berlin, Germany, Aug 31 - Sep 3, 2009.
    
    
    
    Abstract. Earth science research must bridge the gap between the atmosphere and the ocean to foster understanding of Earth's climate and ecology. Typical ocean sensing is done with satellites or in situ buoys and research ships which are slow to reposition. Cloud cover inhibits study of localized transient phenomena such as Harmful Algal Blooms (HAB). A fleet of extended-deployment surface autonomous vehicles will enable in situ study of characteristics of HAB, coastal pollutants, and related phenomena. We have developed a multiplatform telesupervision architecture that supports adaptive reconfiguration based on environmental sensor inputs. Our system allows the autonomous repositioning of smart sensors for HAB study by networking a fleet of NOAA OASIS (Ocean Atmosphere Sensor Integration System) surface autonomous vehicles. In situ measurements intelligently modify the search for areas of high concentration. Inference Grid and complementary information-theoretic techniques support sensor fusion and analysis. Telesupervision supports sliding autonomy from high-level mission tasking, through vehicle and data monitoring, to teleoperation when direct human interaction is appropriate. This paper reports on experimental results from multi-platform tests conducted in the Chesapeake Bay and in Pittsburgh, Pennsylvania waters using OASIS platforms, autonomous kayaks, and multiple simulated platforms to conduct cooperative sensing of chlorophyll-a and water quality.
    
    
71. Robot Boats as a Mobile Aquatic Sensor Network.
    Kian Hsiang Low, Gregg Podnar, Stephen Stancliff, John M. Dolan & Alberto Elfes.
    In Proceedings of the IPSN-09 Workshop on Sensor Networks for Earth and Space Science Applications (ESSA-09), San Francisco, CA, Apr 16, 2009.
    
    
    
    Abstract. This paper describes the Multilevel Autonomy Robot Telesupervision Architecture (MARTA), an architecture for supervisory control of a heterogeneous fleet of net-worked unmanned autonomous aquatic surface vessels carrying a payload of environmental science sensors. This architecture allows a land-based human scientist to effectively supervise data gathering by multiple robotic assets that implement a web of widely dispersed mobile sensors for in situ study of physical, chemical or bio-logical processes in water or in the water/atmosphere interface.
    
    
72. Adaptive Multi-Robot Wide-Area Exploration And Mapping.
    Kian Hsiang Low, John M. Dolan & Pradeep Khosla.
    In Proceedings of the 7th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS-08), pages 23-30, Estoril, Portugal, May 12-16, 2008.
    22.2% acceptance rate
    Also presented as a poster in RSS-09 Workshop on Aquatic Robots and Ocean Sampling, Seattle, WA, Jun 29, 2009.
    
    
    Abstract. The exploration problem is a central issue in mobile robotics. A complete terrain coverage is not practical if the environment is large with only a few small hotspots. This paper presents an adaptive multi-robot exploration strategy that is novel in performing both wide-area coverage and hotspot sampling using non-myopic path planning. As a result, the environmental phenomena can be accurately mapped. It is based on a dynamic programming formulation, which we call the Multi-robot Adaptive Sampling Problem (MASP). A key feature of MASP is in covering the entire adaptivity spectrum, thus allowing strategies of varying adaptivity to be formed and theoretically analyzed in their performance; a more adaptive strategy improves mapping accuracy. We apply MASP to sampling the Gaussian and log-Gaussian processes, and analyze if the resulting strategies are adaptive and maximize wide-area coverage and hotspot sampling. Solving MASP is non-trivial as it comprises continuous state components. So, it is reformulated for convex analysis, which allows discrete-state monotone-bounding approximation to be developed. We provide a theoretical guarantee on the policy quality of the approximate MASP (aMASP) for using in MASP. Although aMASP can be solved exactly, its state size grows exponentially with the number of stages. To alleviate this computational difficulty, anytime algorithms are proposed based on aMASP, one of which can guarantee its policy quality for MASP in real time.
    
    
73. Adaptive Sampling for Multi-Robot Wide-Area Exploration.
    Kian Hsiang Low, Geoffrey J. Gordon, John M. Dolan & Pradeep Khosla.
    In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'07), pages 755-760, Rome, Italy, Apr 10-14, 2007.
    
    
    
    Abstract. The exploration problem is a central issue in mobile robotics. A complete coverage is not practical if the environment is large with a few small hotspots, and the sampling cost is high. So, it is desirable to build robot teams that can coordinate to maximize sampling at these hotspots while minimizing resource costs, and consequently learn more accurately about properties of such environmental phenomena. An important issue in designing such teams is the exploration strategy. The contribution of this paper is in the evaluation of an adaptive exploration strategy called adaptive cluster sampling (ACS), which is demonstrated to reduce the resource costs (i.e., mission time and energy consumption) of a robot team, and yield more information about the environment by directing robot exploration towards hotspots. Due to the adaptive nature of the strategy, it is not obvious how the sampled data can be used to provide unbiased, low-variance estimates of the properties. This paper therefore discusses how estimators that are Rao-Blackwellized can be used to achieve low error. This paper also presents the first analysis of the characteristics of the environmental phenomena that favor the ACS strategy and estimators. Quantitative experimental results in a mineral prospecting task simulation show that our approach is more efficient in exploration by yielding more minerals and information with fewer resources and providing more precise mineral density estimates than previous methods.
    
    
74. Autonomic Mobile Sensor Network with Self-Coordinated Task Allocation and Execution.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In IEEE Transactions on Systems, Man, and Cybernetics - Part C: Applications and Reviews (Special Issue on Engineering Autonomic Systems), volume 36, issue 3, pages 315-327, May 2006.
    Extended version of our IJCAI-03, ICRA'04, and AAAI-04 papers
    Andrew P. Sage Best Transactions Paper Award for the best paper published in IEEE Trans. SMC - Part A, B, and C in 2006
    
    
    Abstract. This paper describes a distributed layered architecture for resource-constrained multirobot cooperation, which is utilized in autonomic mobile sensor network coverage. In the upper layer, a dynamic task allocation scheme self-organizes the robot coalitions to track efficiently across regions. It uses concepts of ant behavior to self-regulate the regional distributions of robots in proportion to that of the moving targets to be tracked in a nonstationary environment. As a result, the adverse effects of task interference between robots are minimized and network coverage is improved. In the lower task execution layer, the robots use self-organizing neural networks to coordinate their target tracking within a region. Both layers employ self-organization techniques, which exhibit autonomic properties such as self-configuring, self-optimizing, self-healing, and self-protecting. Quantitative comparisons with other tracking strategies such as static sensor placements, potential fields, and auction-based negotiation show that our layered approach can provide better coverage, greater robustness to sensor failures, and greater flexibility to respond to environmental changes.
    
    
75. An Ensemble of Cooperative Extended Kohonen Maps for Complex Robot Motion Tasks.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Neural Computation, volume 17, issue 6, pages 1411-1445, Jun 2005.
    Extended version of our AAMAS-02, ICRA'03, and IJCAI-03 papers
    
    
    Abstract. Self-organizing feature maps such as extended Kohonen maps (EKMs) have been very successful at learning sensorimotor control for mobile robot tasks. This letter presents a new ensemble approach, cooperative EKMs with indirect mapping, to achieve complex robot motion. An indirect-mapping EKM self-organizes to map from the sensory input space to the motor control space indirectly via a control parameter space. Quantitative evaluation reveals that indirect mapping can provide finer, smoother, and more efficient motion control than does direct mapping by operating in a continuous, rather than discrete, motor control space. It is also shown to outperform basis function neural networks. Furthermore, training its control parameters with recursive least squares enables faster convergence and better performance compared to gradient descent. The cooperation and competition of multiple self-organized EKMs allow a nonholonomic mobile robot to negotiate unforeseen, concave, closely spaced, and dynamic obstacles. Qualitative and quantitative comparisons with neural network ensembles employing weighted sum reveal that our method can achieve more sophisticated motion tasks even though the weighted-sum ensemble approach also operates in continuous motor control space.
    
    
76. Task Allocation via Self-Organizing Swarm Coalitions in Distributed Mobile Sensor Network.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI-04), pages 28-33, San Jose, CA, Jul 25-29, 2004.
    26.7% acceptance rate
    
    
    Abstract. This paper presents a task allocation scheme via self-organizing swarm coalitions for distributed mobile sensor network coverage. Our approach uses the concepts of ant behavior to self-regulate the regional distributions of sensors in proportion to that of the moving targets to be tracked in a non-stationary environment. As a result, the adverse effects of task interference between robots are minimized and sensor network coverage is improved. Quantitative comparisons with other tracking strategies such as static sensor placement, potential fields, and auction-based negotiation show that our approach can provide better coverage and greater flexibility to respond to environmental changes.
    
    
77. Reactive, Distributed Layered Architecture for Resource-Bounded Multi-Robot Cooperation: Application to Mobile Sensor Network Coverage.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'04), pages 3747-3752, New Orleans, LA, Apr 26 - May 1, 2004.
    
    
    
    Abstract. This paper describes a reactive, distributed layered architecture for cooperation of multiple resource-bounded robots, which is utilized in mobile sensor network coverage. In the upper layer, a dynamic task allocation scheme self-organizes the robot coalitions to track efficiently in separate regions. It uses the concepts of ant behavior to self-regulate the regional distributions of robots in proportion to that of the targets to be tracked in the changing environment. As a result, the adverse effects of task interference between robots are minimized and sensor network coverage is improved. In the lower layer, the robots use self-organizing neural networks to coordinate their target tracking within a region. Quantitative comparisons with other tracking strategies such as static sensor placements, potential fields, and auction-based negotiation show that our approach can provide better coverage and greater flexibility in responding to environmental changes.
    
    
78. Continuous-Spaced Action Selection for Single- and Multi-Robot Tasks Using Cooperative Extended Kohonen Maps.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the IEEE International Conference on Networking, Sensing and Control (ICNSC'04) (Invited Paper to Special Session on Visual Surveillance), pages 198-203, Taipei, Taiwan, Mar 21-23, 2004.
    
    
    
    Abstract. Action selection is a central issue in the design of behavior-based control architectures for autonomous mobile robots. This paper presents an action selection framework based on an assemblage of self-organizing neural networks called Cooperative Extended Kohonen Maps. This framework encapsulates two features that significantly enhance a robot's action selection capability: self-organization in the continuous state and action spaces to provide smooth, efficient and fine motion control; action selection via the cooperation and competition of Extended Kohonen Maps so that more complex motion tasks can be achieved. Qualitative and quantitative comparisons for both single- and multi-robot motion tasks show that our framework can provide better action selection than do action superposition methods.
    
    
79. Action Selection for Single- and Multi-Robot Tasks Using Cooperative Extended Kohonen Maps.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-03), pages 1505-1506, Acapulco, Mexico, Aug 9-15, 2003.
    27.6% acceptance rate
    
    
    Abstract. This paper presents an action selection framework based on an assemblage of self-organizing neural networks called Cooperative Extended Kohonen Maps. This framework encapsulates two features that significantly enhance a robot's action selection capability: self-organization in the continuous state and action spaces to provide smooth, efficient and fine motion control; action selection via the cooperation and competition of Extended Kohonen Maps to achieve more complex motion tasks. Qualitative and quantitative comparisons for single- and multi-robot tasks show our framework can provide better action selection than do potential fields method.
    
    
80. Action Selection in Continuous State and Action Spaces by Cooperation and Competition of Extended Kohonen Maps.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the 2nd International Joint Conference on Autonomous Agents and MultiAgent Systems (AAMAS-03), pages 1056-1057, Melbourne, Australia, Jul 14-18, 2003.
    
    
    
    Abstract. This paper presents an action selection framework based on an assemblage of self-organizing neural networks called Cooperative Extended Kohonen Maps. This framework encapsulates two features that significantly enhance a robot's action selection capability: self-organization in the continuous state and action spaces to provide smooth, efficient and fine motion control; action selection via the cooperation and competition of Extended Kohonen Maps to achieve more complex motion tasks. Qualitative tests demonstrate the capability of our action selection method for both single- and multi-robot motion tasks.
    
    
81. Enhancing the Reactive Capabilities of Integrated Planning and Control with Cooperative Extended Kohonen Maps.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'03), pages 3428-3433, Taipei, Taiwan, May 12-17, 2003.
    
    
    
    Abstract. Despite the many significant advances made in robot motion research, few works have focused on the tight integration of high-level deliberative planning with reactive control at the lowest level. In particular, the real-time performance of existing integrated planning and control architectures is still not optimal because the reactive control capabilities have not been fully realized. This paper aims to enhance the low-level reactive capabilities of integrated planning and control with Cooperative Extended Kohonen Maps for handling complex, unpredictable environments so that the work-load of the high-level planner can be consequently eased. The enhancements include fine, smooth motion control, execution of more complex motion tasks such as overcoming unforeseen concave obstacles and traversing between closely spaced obstacles, and asynchronous execution of behaviors.
    
    
82. A Hybrid Mobile Robot Architecture with Integrated Planning and Control.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the 1st International Joint Conference on Autonomous Agents and MultiAgent Systems (AAMAS-02), pages 219-226, Bologna, Italy, Jul 15-19, 2002.
    26% acceptance rate
    
    
    Abstract. Research in the planning and control of mobile robots has received much attention in the past two decades. Two basic approaches have emerged from these research efforts: deliberative vs. reactive. These two approaches can be distinguished by their different usage of sensed data and global knowledge, speed of response, reasoning capability, and complexity of computation. Their strengths are complementary and their weaknesses can be mitigated by combining the two approaches in a hybrid architecture. This paper describes a method for goal-directed, collision-free navigation in unpredictable environments that employs a behavior-based hybrid architecture with asynchronously operating behavioral modules. It differs from existing hybrid architectures in two important ways: (1) the planning module produces a sequence of checkpoints instead of a conventional complete path, and (2) in addition to obstacle avoidance, the reactive module also performs target reaching under the control of a self-organizing neural network. The neural network is trained to perform fine, smooth motor control that moves the robot through the checkpoints. These two aspects facilitate a tight integration between high-level planning and low-level control, which permits real-time performance and easy path modification even when the robot is en route to the goal position.
    
    
83. Integrated Planning and Control of Mobile Robot with Self-Organizing Neural Network.
    Kian Hsiang Low, Wee Kheng Leow & Marcelo H. Ang, Jr.
    In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'02), pages 3870-3875, Washington, DC, May 11-15, 2002.
    
    
    
    Abstract. Despite the many significant advances made in robotics research, few works have focused on the tight integration of task planning and motion control. Most integration works involve the task planner providing discrete commands to the low-level controller, which performs kinematics and control computations to command the motor and joint actuators. This paper presents a framework of the integrated planning and control for mobile robot navigation. Unlike existing integrated approaches, it produces a sequence of checkpoints instead of a complete path at the planning level. At the motion control level, a neural network is trained to perform motor control that moves the robot from one checkpoint to the next. This method allows for a tight integration between high-level planning and low-level control, which permits real-time performance and easy modification of motion path while the robot is enroute to the goal position.
    

1. Automated Machine Learning: New Advances on Bayesian Optimization.
   Dmitrii Kharkovskii.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, Dec 2020.
   
   
   
   Abstract. Recent advances in Bayesian optimization (BO) have delivered a promising suite of tools for optimizing an unknown expensive to evaluate black-box objective function with a finite budget of evaluations. A significant advantage of BO is its general formulation: BO can be utilized to optimize any black-box objective function. As a result, BO has been applied in a wide range of applications such as automated machine learning, robotics or environmental monitoring, among others. Furthermore, its general formulation makes BO attractive for deployment in new applications. However, potential new applications can have additional requirements not satisfied by the classical BO setting. In this thesis, we aim to address some of these requirements in order to scale up BO technology for the practical use in new real-world applications.
   Firstly, this thesis tackles the problem of data privacy, which is not addressed by the standard setting of BO. Specifically, we consider the outsourced setting where the entity holding the dataset and the entity performing BO are represented by different parties, and the dataset cannot be released non-privately. For example, a hospital holds a dataset of sensitive medical records and outsources the BO task on this dataset to an industrial AI company. We present the private-outsourced-Gaussian process-upper confidence bound (PO-GP-UCB) algorithm, which is the first algorithm for privacy-preserving BO in the outsourced setting with a provable performance guarantee. The key idea of our approach is to make the BO performance of our algorithm similar to that of non-private GP-UCB run using the original dataset, which is achieved by using a random projection-based transformation that preserves both privacy and the pairwise distances between inputs. Our main theoretical contribution is to show that a regret bound similar to that of the standard GP-UCB algorithm can be established for our PO-GP-UCB algorithm. We empirically evaluate the performance of our algorithm with synthetic and real-world datasets.
   Secondly, we consider applications of BO for hotspot sampling in spatially varying phenomena. For such applications, we exploit the structure of the spatially varying phenomenon in order to increase the BO lookahead and, as a result, improve the performance of the algorithm and make it more suitable for practical use in real-world scenarios. To do this, we present a principled multi-staged Bayesian sequential decision algorithm for nonmyopic adaptive BO that, in particular, exploits macro-actions for scaling up to a further lookahead to match up to a larger available budget. To achieve this, we first generalize GP-UCB to a new acquisition function defined with respect to a nonmyopic adaptive macro-action policy, which, unfortunately, is intractable to be optimized exactly due to an uncountable set of candidate outputs. The key novel contribution of our work here is to show that it is in fact possible to solve for a nonmyopic adaptive ε-Bayes-optimal macro-action BO (ε-Macro-BO) policy given an arbitrary user-specified loss bound ε via stochastic sampling in each planning stage which requires only a polynomial number of samples in the length of macro-actions. To perform nonmyopic adaptive BO in real time, we then propose an asymptotically optimal anytime variant of our ε-Macro-BO algorithm with a performance guarantee. Empirical evaluation on synthetic and real-world datasets shows that our proposed approach outperforms existing state-of-the-art algorithms.
   Finally, this thesis proposes a black-box attack for adversarial machine learning based on BO. Since the dimension of the inputs in adversarial learning is usually too high for applying BO directly, our proposed attack applies dimensionality reduction and searches for an adversarial perturbation in a low-dimensional latent space. The key idea of our approach is to automate both the selection of the latent space dimen- sion and the search of the adversarial perturbation in the selected latent space by using BO. Additionally, we use Bayesian optimal stopping to boost the query efficiency of our attack. Performance evaluation using image classification datasets shows that our proposed method outperforms the state-of-the-art black-box adversarial attacks.
   
   
2. New Advances in Bayesian Inference for Gaussian Process and Deep Gaussian Process Models.
   Haibin Yu.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, May 2020.
   
   
   
   Abstract. Machine learning is the study of letting computers learn to perform a specific task in a data-driven manner. In particular, Bayesian machine learning has attracted enor- mous attention mainly due to their ability to provide uncertainty estimates following Bayesian inference. This thesis focuses on Gaussian processes (GPs), a rich class of Bayesian nonparametric models for performing Bayesian machine learning with formal measures of predictive uncertainty.
   However, the applicability of GP in large datasets and in hierarchical composition of GPs is severely limited by computational issues and intractabilities. Therefore, it is crucial to develop accurate and efficient inference algorithms to address these challenges. To this end, this thesis aims at proposing a series of novel approximate Bayesian inference methods for a wide variety of GP models, which unifies the previous literatures, significantly extends them and hopefully lays the foundation for future inference methods.
   To start with, this thesis presents a unifying perspective of existing inducing variables-based GP models, sparse GP (SGP) models and variational inference for SGP models (VSGP). Then, to further mitigate the issue of overfitting during optimization, we present a novel variational inference framework for deriving a family of Bayesian SGP regression models, referred to as variational Bayesian SGP (VBSGP) regression models.
   Next, taking into account the fact that the expressiveness of GP and SGP depends heavily on the design of the kernel function, we further extend the expressive power of GP by introducing Deep GP (DGP), which is a hierarchical composition of GP models. Unfortunately, exact inference in DGP is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. However, the deterministic approximation methods yield a biased posterior belief while the stochastic one is computationally costly. In this regard, we present the implicit posterior variational inference (IPVI) framework for DGPs that can ideally recover an unbiased posterior belief and still preserve time efficiency. Inspired by generative adversarial networks, our IPVI framework casts the DGP inference problem as a two- player game in which a Nash equilibrium, interestingly, coincides with an unbiased posterior belief.
   We hope this thesis at least provides additional confidence and clarity for researchers who are devoting themselves to Bayesian nonparametric models, Gaussian process models in particular. Moreover, we also wish this thesis to offer inspirations for future works, and some thoughts that could be useful for future solutions.
   
   
3. Data-Efficient Machine Learning with Multiple Output Types and High Input Dimensions.
   Yehong Zhang.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, Dec 2017.
   
   
   
   Abstract. Recent research works in machine learning (ML) have focused on learning some target variables of interest to achieve competitive (or state-of-the-art) predictive performance in less time but without requiring large quantities of data, which is known as data-efficient ML. This thesis focuses on two important data-efficient ML approaches: active learning (AL) and Bayesian optimization (BO) which, instead of learning passively from a given small set of data, need to select and gather the most informative observations for learning the target variables of interest more accurately given some budget constraints. To advance the state-of-the-art of data-efficient ML, novel generalizations of AL and BO algorithms are proposed in this thesis for addressing the issues arising from multiple output types and high input dimensions which are the practical settings in many real-world applications.
   In particular, this thesis aims to (a) exploit the auxiliary types of outputs which usually coexist and correlate well with the target output types, and more importantly, are less noisy and/or less tedious to sample for improving the learning performance of the target output type in both AL and BO algorithms and (b) scale up the state-of-the-art BO algorithm to high input dimensions. To achieve this, the specific data with multiple output types or high input dimensions is represented using some form of Gaussian process (GP)-based probabilistic regression models which allow the predictive uncertainty of the outputs to be formally quantified and consequently exploited for developing efficient AL and BO algorithms.
   To achieve above objectives, an AL algorithm of multi-output GP (MOGP) is first developed for minimizing the predictive uncertainty (i.e., posterior joint entropy) of the target output type. In contrast to existing works, our AL problems involve selecting not just the most informative sampling inputs to be observed but also the types of outputs at each selected input for improving the learning performance of only the target output type given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling inputs and selected observations when optimized. To resolve this issue, we exploit a structure common to sparse MOGP models for deriving a novel AL criterion. Furthermore, we exploit a relaxed form of submodularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for AL of MOGP and single-output GP models.
   Secondly, to boost the BO performance by exploiting the cheaper and/or less noisy observations of some auxiliary functions with varying fidelities, we proposed a novel generalization of predictive entropy search (PES) for multi-fidelity BO called multi-fidelity PES (MF-PES). In contrast to existing multi-fidelity BO algorithms, our proposed MF-PES algorithm can naturally trade off between exploitation vs. exploration over the target and auxiliary functions with varying fidelities without needing to manually tune any such parameters. To achieve this, we model the unknown target and auxiliary functions jointly as a convolved MOGP (CMOGP) whose convolutional structure is exploited to formally characterize the fidelity of each auxiliary function through its cross-correlation with the target function. Although the exact acquisition function of MF-PES cannot be computed in closed form, we show that it is in fact possible to derive an efficient approximation of MF-PES via a novel multi-output random features approximation of the CMOGP model whose cross-correlation (i.e., multi-fidelity) structure between the target and auxiliary functions can be exploited for improving the belief of the global target maximizer using the observations from evaluating these functions. Practical constraints are proposed to relate the global target maximizer to that of auxiliary functions. Empirical evaluation on synthetic and real-world experiments shows that MF-PES outperforms the state-of-the-art multi-fidelity BO algorithms.
   Lastly, to improve the BO performance in real-world applications with high input dimensions (e.g., computer vision, biology), we generalize PES for high-dimensional BO by exploiting an additive structure of the target function. New practical constraints are proposed and approximated efficiently such that the proposed acquisition function of additive PES (add-PES) can be optimized independently for each local and low-dimensional input component. The empirical results show that our add-PES considerably improves the performance of the state-of-the-art high-dimensional BO algorithms by using a simple and common setting for optimizing different tested functions with varying input dimensions, which makes it a superior alternative to existing high-dimensional BO algorithms.
   
   
4. Exploiting Decentralized Multi-Agent Coordination for Large-Scale Machine Learning Problems.
   Ruofei Ouyang.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, Dec 2016.
   
   
   
   Abstract. Nowadays, the scale of machine learning problems becomes much larger than before. It raises a huge demand in distributed perception and distributed computation. A multi-agent system provides exceptional scalability for problems like active sensing and data fusion. However, many rich characteristics of large-scale machine learning problems have not been addressed yet such as large input domain, nonstationarity, and high dimensionality. This thesis identifies the challenges related to these characteristics from multi-agent perspective. By exploiting the correlation structure of data in large-scale problems, we propose multi-agent coordination schemes that can improve the scalability of the machine learning models while preserving the computation accuracy. To elaborate, the machine learning problems we are solving with multi-agent coordination techniques are:
   
   

   1. Gaussian process regression. To perform distributed regression on a large-scale environmental phenomenon, data compression is often required due to the communication costs. Currently, decentralized data fusion methods encapsulate the data into local summaries based on a fixed support set. However in a large-scale field, this fixed support set, acting as a centralized component in the decentralized system, cannot approximate the correlation structure of the entire phenomenon well. It leads to evident losses in data summarization. Consequently, the regression performance will be significantly reduced. In order to approximate the correlation structure accurately, we propose an agent-centric support set to allow every agent in the data fusion system to choose a possibly different support set and dynamically switch to another one during execution for encapsulating its own data into a local summary which, perhaps surprisingly, can still be assimilated with the other agents’ local summaries into a globally consistent summary. Together with an information sharing mechanism we designed, the new decentralized data fusion methods with agent-centric support set can be applied to regression problems on a much larger environmental phenomenon with high performance.
   2. Active learning. In the context of environmental sensing, active learning/active sensing is a process of taking observations to minimize the uncertainty in an environmental field. The uncertainty is quantified based on the correlation structure of the phenomenon which is traditionally assumed to be stationary for computational sake. In a large-scale environmental field, this stationary assumption is often violated. Therefore, existing active sensing algorithms perform sub-optimally for a nonstationary environmental phenomenon. To the best of our knowledge, our decentralized multi-robot active sensing (DEC-MAS) algorithm is the first work to address nonstationarity issue in the context of active sensing. The uncertainty in the phenomenon is quantified based on the nonstationary correlation structure estimated by Dirichlet process mixture of Gaussian processes. Further, our DEC-MAS algorithm can efficiently coordinate the exploration of multiple robots to automatically trade-off between learning the unknown, nonstationary correlation structure and minimizing the uncertainty of the environmental phenomenon. It enables multi-agent active sensing techniques to be applied to a large-scale nonstationary environmental phenomenon.
   3. Bayesian optimization. Optimizing an unknown objective function is challenging for traditional optimization methods. Alternatively, in this situation, people use Bayesian optimization which is a modern optimization technique that can optimize a function by only utilizing the observation information (input and output values) collected through simulations. When the input dimension of the function is low, a few simulated observations can generate good result already. However, for high dimensional function, a huge number of observations are required which is impractical when the simulation consumes lots of time and resources.
      Fortunately, many high dimensional problems have sparse correlation structure. Our ANOVA-DCOP work can decompose the correlation structure in the original high-dimensional problem into many correlation structures of subsets of dimensions based on ANOVA kernel function. It significantly reduces the size of input space into a collection of lower-dimensional subspaces. Additionally, we reformulate the Bayesian optimization problem as a decentralized constrained optimization problem (DCOP) that can be efficiently solved by multi-agent coordination techniques so that it can scale up to problems with hundreds of dimensions.

   
   
5. New Advances on Bayesian and Decision-Theoretic Approaches for Interactive Machine Learning.
   Trong Nghia Hoang.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, Feb 2015.
   
   
   
   Abstract. The exploration-exploitation trade-off is a fundamental dilemma in many interactive learning scenarios which include both aspects of reinforcement learning (RL) and active learning (AL): An autonomous agent, situated in an unknown environment, has to actively extract knowledge from the environment by taking actions (or conducting experiments) based on its previously collected information to make accurate predictions or to optimize some utility functions. Thus, to make the most effective use of their resource-constrained budget (e.g., processing time, experimentation cost), the agent must choose carefully between (a) exploiting options (e.g., actions, experiments) which are recommended by its current, possibly incomplete model of the environment, and (b) exploring the other ostensibly sub-optimal choices to gather more information.
   For example, an RL agent has to face a dilemma between (a) exploiting the most-rewarding action according to the current statistical model of the environment at the risk of running into catastrophic situations if the model is not accurate, and (b) exploring a sub-optimal action to gather more information so as to improve the model's accuracy at the potential price of losing the short-term reward. Similarly, an AL algorithm/agent has to consider between (a) conducting the most informative experiments according to its current estimation of the environment model's parameters (i.e., exploitation), and (b) running experiments that help improving the estimation accuracy of these parameters (i.e., exploration).
   More often, learning strategies that ignore exploration will likely exhibit sub-optimal performance due to their imperfect knowledge while, conversely, those that entirely focus on exploration might suffer the cost of learning without benefitting from it. Therefore, a good exploration-exploitation trade-off is critical to the success of those interactive learning agents: In order to perform well, they must strike the right balance between these two conflicting objectives. Unfortunately, while this trade-off has been well-recognized since the early days of RL, the studies of exploration-exploitation have mostly been developed for theoretical settings in the respective field of RL and, perhaps surprisingly, glossed over in the existing AL literature. From a practical point of view, we see three limiting factors:
   
   

   1. Previous works addressing the exploration-exploitation trade-off in RL have largely focused on simple choices of the environment model and consequently, are not practical enough to accommodate real-world applications that have far more complicated environment structures. In fact, we find that most recent advances in Bayesian reinforcement learning (BRL) have only been able to analytically trade off between exploration and exploitation under a simple choice of models such as Flat-Dirichlet-Multinomial (FDM) whose independence and modeling assumptions do not hold for many real-world applications.
   2. Nearly all of the notable works in the AL literature primarily advocate the use of greedy/myopic algorithms whose rates of convergence (i.e., the number of experiments required by the learning algorithm to achieve a desired performance in the worst case) are provably minimax optimal for simple classes of learning tasks (e.g., threshold learning). While these results have greatly ad- vanced our understanding about the limit of myopic AL in worst-case scenarios, significantly less is presently known about whether it is possible to devise nonmyopic AL strategies which optimize the exploration-exploitation trade-off to achieve the best expected performance in budgeted learning scenarios.
   3. The issue of scalability of the existing predictive models (e.g., Gaussian processes) used in AL has generally been underrated since the majority of literature considers small-scale environments which only consist of a few thousand candidate experiments to be selected by single-mode AL algorithms one at a time prior to retraining the model. In contrast, large-scale environments usually have a massive set of million candidate experiments among which tens or hundreds of thousands should be actively selected for learning. For such data-intensive problems, it is often more cost-effective to consider batch-mode AL algorithms which select and conduct multiple experiments in parallel at each stage to collect observations in batch. Retraining the predictive model after incorporating each batch of observations then becomes a computational bottleneck as the collected dataset at each stage quickly grows up to tens or even hundreds of thousand data points.

   
   This thesis outlines some recent progresses that we have been able to make while working toward satisfactory answers to the above challenges, along with practical algorithms that achieve them:
   
   

   1. In particular, in order to put BRL into practice for more complicated and practical problems, we propose a novel framework called Interactive Bayesian Reinforcement Learning (I-BRL) to integrate the general class of parametric models and model priors, thus allowing the practitioners' domain knowledge to be exploited to produce a fine-grained and compact representation of the environment as often required in many real-world applications. Interestingly, we show how the nonmyopic Bayes-optimal policy can be derived analytically by solving I-BRL exactly and propose an approximation algorithm to compute it efficiently in polynomial time. Our empirical studies show that the proposed approach performs competitively with the existing state-of-the-art algorithms.
   2. Then, to establish a theoretical foundation for the exploration-exploitation trade-off in single-mode active learning scenarios with resource-constrained budgets, we present a novel ϵ-Bayes-optimal Decision-Theoretic Active Learning (ϵ-BAL) framework which advocates the use of differential entropy as a performance measure and consequently, derives a learning policy that can approximate the optimal expected performance arbitrarily closely (i.e., within an arbitrary loss bound ϵ). To meet the real-time requirement in time-critical applications, we then propose an asymptotically ϵ-optimal, branch-and-bound anytime algorithm based on ϵ-BAL with performance guarantees. In practice, we empirically demonstrate with both synthetic and real-world datasets that the proposed approach outperforms the state-of-the-art algorithms in budgeted scenarios.
   3. Lastly, to facilitate the future developments of large-scale, nonmyopic AL applications, we further introduce a highly scalable family of anytime predictive models for AL which provably converge toward a well-known class of sparse Gaussian processes (SGPs). Unlike the existing predictive models of AL which cannot be updated incrementally and are only capable of processing middle-sized datasets (i.e., a few thousands of data points), our proposed models can process massive datasets in an anytime fashion, thus providing a principled trade-off between the processing time and the predictive accuracy. The efficiency of our framework is then demonstrated empirically on a variety of large-scale real-world datasets which contains hundreds of thousand data points.

   
   
6. Gaussian Process-Based Decentralized Data Fusion and Active Sensing Agents: Towards Large-Scale Modeling and Prediction of Spatiotemporal Traffic Phenomena.
   Jie Chen.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, Dec 2013.
   
   
   
   Abstract. Knowing and understanding the environmental phenomena is important to many real world applications. This thesis is devoted to study large-scale modeling and prediction of spatiotemporal environmental phenomena (i.e., urban traffic phenomena). Towards this goal, our proposed approaches rely on a class of Bayesian non-parametric models: Gaussian processes (GP).
   To accurately model spatiotemporal urban traffic phenomena in real world situation, a novel relational GP taking into account both the road segment features and road network topology information is proposed to model real world traffic conditions over road network. Additionally, a GP variant called log-Gaussian process (lGP) is exploited to model an urban mobility demand pattern which contains skewness and extremity in demand measurements.
   To achieve efficient and scalable urban traffic phenomenon prediction given a large phenomenon data, we propose three novel parallel GPs: parallel partially independent training conditional (pPITC), parallel partially independent conditional(pPIC) and parallel incomplete Cholesky factorization (pICF)-based approximations of GP model, which can distribute their computational load into a cluster of parallel/multi-core machines, thereby achieving time efficiency. The predictive performances of such parallel GPs are theoretically guaranteed to be equivalent to that of some centralized approaches to approximate full/exact GP regression. The proposed parallel GPs are implemented using the message passing interface (MPI) framework and tested on two large real world datasets. The theoretical and empirical results show that our parallel GPs achieve significantly better time efficiency and scalability than that of full GP, while achieving comparable accuracy. They also achieve fine speedup performance that is the ratio of time required by the parallel algorithms and their centralized counterparts.
   To exploit active mobile sensors to perform decentralized perception of the spatiotemporal urban traffic phenomenon, we propose a decentralized algorithm framework: Gaussian process-based decentralized data fusion and active sensing (D2FAS) which is composed of a decentralized data fusion (DDF) component and a decentralized active sensing (DAS) component. The DDF component includes a novel Gaussian process-based decentralized data fusion (GP-DDF) algorithm that can achieve remarkably efficient and scalable prediction of phenomenon and a novel Gaussian process-based decentralized data fusion with local augmentation (GP-DDF+) algorithm that can achieve better predictive accuracy while preserving time efficiency of GP-DDF. The predictive performances of both GP-DDF and GP-DDF+ are theoretically guaranteed to be equivalent to that of some sophisticated centralized sparse approximations of exact/full GP. For the DAS component, we propose a novel partially decentralized active sensing (PDAS) algorithm that exploits property in correlation structure of GP-DDF to enable mobile sensors cooperatively gathering traffic phenomenon data along a near-optimal joint walk with theoretical guarantee, and a fully decentralized active sensing (FDAS) algorithm that guides each mobile sensor gather phenomenon data along its locally optimal walk.
   Lastly, to justify the practicality of the D2FAS framework, we develop and test D2FAS algorithms running with active mobile sensors on real world datasets for monitoring traffic conditions and sensing/servicing urban mobility demands. Theoretical and empirical results show that the proposed algorithms are significantly more time-efficient, more scalable in the size of data and in the number of sensors than the state-of-the-art centralized approaches, while achieving comparable predictive accuracy.
   
   
7. A Decision-Theoretic Approach for Controlling and Coordinating Multiple Active Cameras in Surveillance.
   Prabhu Natarajan.
   Ph.D. Thesis, Department of Computer Science, National University of Singapore, Dec 2013.
   
   
   
   Abstract. The use of active cameras in surveillance is becoming increasingly popular as they try to meet the demands of capturing high-resolution images/videos of targets in surveillance for face recognition, target identification, forensic video analysis, etc. These active cameras are endowed with pan, tilt, and zoom capabilities, which can be exploited to provide high-quality surveillance. In order to achieve effective, real-time surveillance, an efficient collaborative mechanism is needed to control and coordinate these cameras' actions, which is the focus of this thesis. The central problem in surveillance is to monitor a set of targets with guaranteed image resolution. Controlling and coordinating multiple active cameras to achieve this surveillance task is non-trivial and challenging because: (a) presence of inherent uncertainties in the surveillance environment (targets motion, location, and noisy camera observation); (b) there exists a non-trivial trade-off between number of targets and the resolution of observing these targets; and (c) more importantly, the coordination framework should be scalable with increasing number of targets and cameras.
   In this thesis, we formulate a novel decision-theoretic multi-agent planning approach for controlling and coordinating multiple active cameras in surveillance. Our decision-theoretic approach offers advantages of (a) accounting the uncertainties using probabilistic models; (b) the non-trivial trade-off is addressed by coordinating the active cameras' actions to maximize the number of targets with guaranteed resolution; and (c) the scalability in number of targets and cameras is achieved by exploiting the structures and properties that are present in our surveillance problem. We focus on two novel problems in active camera surveillance: (a) maximizing observations of multiple targets (MOMT), i.e., maximizing the number of targets observed in active cameras with guaranteed image resolution; and (b) improving fairness in observation of multiple targets (FOMT), i.e., no target is "starved" of observation by active cameras for long duration of time.
   We propose two formal decision-theoretic frameworks (a) Markov Decision Process (MDP) and (b) Partially Observable Markov Decision Process (POMDP) frameworks for coordinating active cameras in surveillance. MDP framework controls active cameras in fully observable surveillance environments where the active cameras are supported by one or more wide-view static/fixed cameras to observe the entire surveillance environment at low-resolution. POMDP framework controls active cameras in partially observable surveillance environments where it is impractical to observe the entire surveillance environment using static/fixed cameras due to occlusions caused by physical infrastructures. Hence the POMDP framework do not have a complete view of the surveillance environment.
   Specifically, we propose (a) MDP frameworks to solve MOMT problem and FOMT problem in fully observable surveillance environment; and (b) POMDP framework to solve MOMT problem in partially observable surveillance environment. As proven analytically, our MDP and POMDP frameworks incurs time that is linear in number of targets to be observed during surveillance. We have used max-plus algorithm with our MDP framework to improve its scalability in number of cameras for MOMT problem. Empirical evaluation through simulations in realistic surveillance environment reveals that our proposed approach can achieve high-quality surveillance in real time. We also demonstrate our pro- posed approach with real Axis 214 PTZ cameras to show the practicality of our approach in real world surveillance. Both the simulations and real camera experiments show that our decision-theoretic approach can control and coordinate active cameras efficiently and hence contributes significantly towards improving the active camera surveillance research.
   
   
8. Information-Theoretic Multi-Robot Path Planning.
   Nannan Cao.
   M.Sc. Thesis, Department of Computer Science, National University of Singapore, Sep 2012.
   
   
   
   Abstract. Research in environmental sensing and monitoring is especially important in supporting environmental sustainability efforts worldwide, and has recently attracted significant attention and interest. A key direction of this research lies in modeling and predicting the spatiotemporally varying environmental phenomena. One approach is to use a team of robots to sample the area and model the measurement values at unobserved points. For smoothly varying and hotspot fields, there is some work which has been done to model the fields well. However, there is still a class of common environmental fields called anisotropic fields in which the spatial phenomena are highly correlated along one direction and less correlated along the perpendicular direction. We exploit the environmental structure to improve the sampling performance and time efficiency of planning for anisotropic fields.
   In this thesis, we cast the planning problem into a stagewise decision-theoretic problem. we adopt Gaussian Process to model spatial phenomena. Maximum entropy criterion and maximum mutual information criterion are used to measure the informativeness of the observation paths. It is found that for many GPs, correlation of two points exponentially decreases with the distance between the two points. With this property, for maximum entropy criterion, we propose a polynomial-time approximation algorithm, MEPP, to find the maximum entropy paths. We also provide a theoretical performance guarantee for this algorithm. For maximum mutual information criterion, we propose another polynomial-time approximation algorithm, M2IPP. Similar to the MEPP, a performance guarantee is also provided for this algorithm. We demonstrate the performance advantages of our algorithms on two real data sets. To get lower prediction error, three priciples have also been proposed to select the criterion for different environmental fields.
   
   
9. Multi-Robot Adaptive Exploration and Mapping for Environmental Sensing Applications.
   Kian Hsiang Low.
   Ph.D. Thesis, Technical Report CMU-ECE-2009-024, Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, Aug 2009.
   
   
   
   Abstract. Recent research in robot exploration and mapping has focused on sampling hotspot fields, which often arise in environmental and ecological sensing applications. Such a hotspot field is characterized by continuous, positively skewed, spatially correlated measurements with the hotspots exhibiting extreme measurements and much higher spatial variability than the rest of the field.
   To map a hotspot field of the above characterization, we assume that it is realized from non-parametric probabilistic models such as the Gaussian and log-Gaussian processes (respectively, GP and lGP), which can provide formal measures of map uncertainty. To learn a hotspot field map, the exploration strategy of a robot team then has to plan resource-constrained observation paths that minimize the uncertainty of a spatial model of the hotspot field. This exploration problem is formalized in a sequential decision-theoretic planning under uncertainty framework called the multi-robot adaptive sampling problem (MASP). So, MASP can be viewed as a sequential, non-myopic version of active learning. In contrast to finite-state Markov decision problems, MASP adopts a more complex but realistic continuous-state, non-Markovian problem structure so that its induced exploration policy can be informed by the complete history of continuous, spatially correlated observations for selecting paths. It is unique in unifying formulations of non-myopic exploration problems along the entire adaptivity spectrum, thus subsuming existing non-adaptive formulations and allowing the performance advantage of a more adaptive policy to be theoretically realized. Through MASP, it is demonstrated that a more adaptive strategy can exploit clustering phenomena in a hotspot field to produce lower expected map uncertainty. By measuring map uncertainty using the mean-squared error criterion, a MASP-based exploration strategy consequently plans adaptive observation paths that minimize the expected posterior map error or equivalently, maximize the expected map error reduction.
   The time complexity of solving MASP (approximately) depends on the map resolution, which limits its practical use in large-scale, high-resolution exploration and mapping. This computational difficulty is alleviated through an information-theoretic approach to MASP (iMASP), which measures map uncertainty based on the entropy criterion instead. As a result, an iMASP-based exploration strategy plans adaptive observation paths that minimize the expected posterior map entropy or equivalently, maximize the expected entropy of observation paths. Unlike MASP, reformulating the cost-minimizing iMASP as a reward-maximizing dual problem causes its time complexity of being solved approximately to be independent of the map resolution and less sensitive to larger robot team size as demonstrated both analytically and empirically. Furthermore, this reward-maximizing dual transforms the widely-used non-adaptive maximum entropy sampling problem into a novel adaptive variant, thus improving the performance of the induced exploration policy.
   One advantage stemming from the reward-maximizing dual formulations of MASP and iMASP is that they allow observation selection properties of the induced exploration policies to be realized for sampling the hotspot field. These properties include adaptivity, hotspot sampling, and wide-area coverage. We show that existing GP-based exploration strategies may not explore and map the hotspot field well with the selected observations because they are non-adaptive and perform only wide-area coverage. In contrast, the lGP-based exploration policies can learn a high-quality hotspot field map because they are adaptive and perform both wide-area coverage and hotspot sampling.
   The other advantage is that even though MASP and iMASP are non-trivial to solve due to their continuous state components, the convexity of their reward-maximizing duals can be exploited to derive, in a computationally tractable manner, discrete-state monotone-bounding approximations and subsequently, approximately optimal exploration policies with theoretical performance guarantees. Anytime algorithms based on approximate MASP and iMASP are then proposed to alleviate the computational difficulty that arises from their non-Markovian structure.
   It is of practical interest to be able to quantitatively characterize the "hotspotness" of an environmental field. We propose a novel "hotspotness" index, which is defined in terms of the spatial correlation properties of the hotspot field. As a result, this index can be related to the intensity, size, and diffuseness of the hotspots in the field.
   We also investigate how the spatial correlation properties of the hotspot field affect the performance advantage of adaptivity. In particular, we derive sufficient and necessary conditions of the spatial correlation properties for adaptive exploration to yield no performance advantage.
   Lastly, we develop computationally efficient approximately optimal exploration strategies for sampling the GP by assuming the Markov property in iMASP planning. We provide theoretical guarantees on the performance of the Markov-based policies, which improve with decreasing spatial correlation. We evaluate empirically the effects of varying spatial correlations on the mapping performance of the Markov-based policies as well as whether these Markov-based path planners are time-efficient for the transect sampling task.
   Through the abovementioned work, this thesis establishes the following two claims: (1) adaptive, non-myopic exploration strategies can exploit clustering phenomena to plan observation paths that produce lower map uncertainty than non-adaptive, greedy methods; and (2) Markov-based exploration strategies can exploit small spatial correlation to plan observation paths which achieve map uncertainty comparable to that of non-Markovian policies using significantly less planning time.
   
   
10. Adaptive Sampling for Multi-Robot Wide Area Prospecting.
    Kian Hsiang Low, Geoffrey J. Gordon, John M. Dolan, and Pradeep Khosla.
    In Technical Report CMU-RI-TR-05-51, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, Oct 2005.
    
    
    
    Abstract. Prospecting for in situ mineral resources is essential for establishing settlements on the Moon and Mars. To reduce human effort and risk, it is desirable to build robotic systems to perform this prospecting. An important issue in designing such systems is the sampling strategy: how do the robots choose where to prospect next? This paper argues that a strategy called Adaptive Cluster Sampling (ACS) has a number of desirable properties: compared to conventional strategies, (1) it reduces the total mission time and energy consumption of a team of robots, and (2) returns a higher mineral yield and more information about the prospected region by directing exploration towards areas of high mineral density, thus providing detailed maps of the boundaries of such areas. Due to the adaptive nature of the sampling scheme, it is not immediately obvious how the resulting sampled data can be used to provide an unbiased, low-variance estimate of the regional mineral density. This paper therefore investigates new mineral density estimators, which have lower error than previously-developed estimators; they are derived from the older estimators via a process called Rao-Blackwellization. Since the efficiency of estimators depends on the type of mineralogical population sampled, the population characteristics that favor ACS estimators are also analyzed. The ACS scheme and our new estimators are evaluated empirically in a detailed simulation of the prospecting task, and the quantitative results show that our approach can yield more minerals with less resources and provide more accurate mineral density estimates than previous methods.
    
    
11. Integrated Robot Planning and Control with Extended Kohonen Maps.
    Kian Hsiang Low.
    M.Sc. Thesis, Department of Computer Science, School of Computing, National University of Singapore, Jul 2002.
    Singapore Computer Society Prize for best M.Sc. Thesis 2002-2003
    
    
    Abstract. The problem of goal-directed, collision-free motion in a complex, unpredictable environment can be solved by tightly integrating high-level deliberative planning with low-level reactive control. This thesis presents two such architectures for a nonholonomic mobile robot. To achieve real-time performance, reactive control capabilities have to be fully realized so that the deliberative planner can be simplified. These architectures are enriched with reactive target reaching and obstacle avoidance modules. Their target reaching modules use indirect-mapping Extended Kohonen Map to provide finer and smoother motion control than direct-mapping methods. While one architecture fuses these modules indirectly via command fusion, the other one couples them directly using cooperative Extended Kohonen Maps, enabling the robot to negotiate unforeseen concave obstacles. The planner for both architectures use a slippery cells technique to decompose the free workspace into fewer cells, thus reducing search time. Any two points in the cell can still be traversed by reactive motion.
    
    
12. Mobile Robots That Learn to Navigate.
    Kian Hsiang Low.
    Honors Thesis, Department of Computer Science, School of Computing, National University of Singapore, Apr 2001.
    
    
    
    Abstract. A sensorimotor controller has been implemented to enable a mobile robot to learn its motion control autonomously and perform simple target-reaching movements. This controller is able to perform fine motion by reducing its self-positioning error and also, reach a designated target location with minimum delay. The control architecture is in the form of a neural network known as the Self-Organizing Map. Besides implementing the motor control and the online learning algorithms, the essentiality of a pre-learning phase is also evaluated. Then, we explore the possibility of incorporating a novel concept known as Local Linear Smoothing into our batch training algorithm; this notion allows the elimination of the boundary bias phenomenon. Lastly, we suggest a simple approach to learning in an obstacle-ridden environment.
    
    

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