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We consider the networked multi-agent reinforcement learning (MARL) problem in a fully decentralized setting, where agents learn to coordinate to achieve the joint success. This problem is widely encountered in many areas including traffic control, distributed control, and smart grids. We assume that the reward function for each agent can be different and observed only locally by the agent itself. Furthermore, each agent is located at a node of a communication network and can exchanges information only with its neighbors. Using softmax temporal consistency and a decentralized optimization method, we obtain a principled and data-efficient iterative algorithm. In the first step of each iteration, an agent computes its local policy and value gradients and then updates only policy parameters. In the second step, the agent propagates to its neighbors the messages based on its value function and then updates its own value function. Hence we name the algorithm value propagation. We prove a non-asymptotic convergence rate 1/T with the nonlinear function approximation. To the best of our knowledge, it is the first MARL algorithm with convergence guarantee in the control, off-policy and non-linear function approximation setting. We empirically demonstrate the effectiveness of our approach in experiments.

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time series characteristics exhibiting in real-world data which are not addressed properly, including 1) ability to handle seasonality fluctuation and shift, and abrupt change in trend and reminder; 2) robustness on data with anomalies; 3) applicability on time series with long seasonality period. In the paper, we propose a novel and generic time series decomposition algorithm to address these challenges. Specifically, we extract the trend component robustly by solving a regression problem using the least absolute deviations loss with sparse regularization. Based on the extracted trend, we apply the the non-local seasonal filtering to extract the seasonality component. This process is repeated until accurate decomposition is obtained. Experiments on different synthetic and real-world time series datasets demonstrate that our method outperforms existing solutions., Comment: Accepted to the thirty-third AAAI Conference on Artificial Intelligence (AAAI 2019), 9 pages, 5 figures

Motivated by applications in clinical trials and finance, we study the problem of online convex optimization (with bandit feedback) where the decision maker is risk-averse. We provide two algorithms to solve this problem. The first one is a descent-type algorithm which is easy to implement. The second algorithm, which combines the ellipsoid method and a center point device, achieves (almost) optimal regret bounds with respect to the number of rounds. To the best of our knowledge this is the first attempt to address risk-aversion in the online convex bandit problem.

We study the online saddle point problem, an online learning problem where at each iteration a pair of actions need to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the gap between the cumulative payoffs and the saddle point value of the aggregate payoff function, which we measure using a metric called "SP-Regret". The problem generalizes the online convex optimization framework but here we must ensure both players incur cumulative payoffs close to that of the Nash equilibrium of the sum of the games. We propose an algorithm that achieves SP-Regret proportional to $\sqrt{\ln(T)T}$ in the general case, and $\log(T)$ SP-Regret for the strongly convex-concave case. We also consider the special case where the payoff functions are bilinear and the decision sets are the probability simplex. In this setting we are able to design algorithms that reduce the bounds on SP-Regret from a linear dependence in the dimension of the problem to a \textit{logarithmic} one. We also study the problem under bandit feedback and provide an algorithm that achieves sublinear SP-Regret. We then consider an online convex optimization with knapsacks problem motivated by a wide variety of applications such as: dynamic pricing, auctions, and crowdsourcing. We relate this problem to the online saddle point problem and establish $O(\sqrt{T})$ regret using a primal-dual algorithm.

We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered around the empirical distribution defined via Wasserstein metric, thus our approach is data-driven and free of distributional assumptions. We develop a convex safe approximation of the minimax formulation and show that such approximation renders a nearly-optimal detector among the family of all possible tests. By exploiting the structure of the least favorable distribution, we also develop a tractable reformulation of such approximation, with complexity independent of the dimension of observation space and can be nearly sample-size-independent in general. Real-data example using human activity data demonstrated the excellent performance of the new robust detector.

Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to $\log(\frac{1}{\epsilon})$ for the smooth and strongly convex objective. This complexity result is especially significant in learning problem, as the overwhelming data size makes a single evluation of gradient computational expensive. However, in high-dimensional statistical estimation problems, the objective is typically not strongly convex, and sometimes even non-convex. In this paper, we extend the state-of-the-art FW type algorithms for the large-scale, high-dimensional estimation problem. We show that as long as the objective satisfies {\em restricted strong convexity}, and we are not optimizing over statistical limit of the model, the $\log(\frac{1}{\epsilon})$ gradient evaluation complexity could still be attained.

Distributed optimization has gained a surge of interest in recent years. In this paper we propose a distributed projection free algorithm named Distributed Conditional Gradient Sliding(DCGS). Compared to the state-of-the-art distributed Frank-Wolfe algorithm, our algorithm attains the same communication complexity under much more realistic assumptions. In contrast to the consensus based algorithm, DCGS is based on the primal-dual algorithm, yielding a modular analysis that can be exploited to improve linear oracle complexity whenever centralized Frank-Wolfe can be improved. We demonstrate this advantage and show that the linear oracle complexity can be reduced to almost the same order of magnitude as the communication complexity, when the feasible set is polyhedral. Finally we present experimental results on Lasso and matrix completion, demonstrating significant performance improvement compared to the existing distributed Frank-Wolfe algorithm.

We devise a distributional variant of gradient temporal-difference (TD) learning. Distributional reinforcement learning has been demonstrated to outperform the regular one in the recent study \citep{bellemare2017distributional}. In the policy evaluation setting, we design two new algorithms called distributional GTD2 and distributional TDC using the Cram{\'e}r distance on the distributional version of the Bellman error objective function, which inherits advantages of both the nonlinear gradient TD algorithms and the distributional RL approach. In the control setting, we propose the distributional Greedy-GQ using the similar derivation. We prove the asymptotic almost-sure convergence of distributional GTD2 and TDC to a local optimal solution for general smooth function approximators, which includes neural networks that have been widely used in recent study to solve the real-life RL problems. In each step, the computational complexities of above three algorithms are linear w.r.t.\ the number of the parameters of the function approximator, thus can be implemented efficiently for neural networks.

In this paper, a multi-state diagnosis and prognosis (MDP) framework is proposed for tool condition monitoring via a deep belief network based multi-state approach (DBNMS). For fault diagnosis, a cost-sensitive deep belief network (namely ECS-DBN) is applied to deal with the imbalanced data problem for tool state estimation. An appropriate prognostic degradation model is then applied for tool wear estimation based on the different tool states. The proposed framework has the advantage of automatic feature representation learning and shows better performance in accuracy and robustness. The effectiveness of the proposed DBNMS is validated using a real-world dataset obtained from the gun drilling process. This dataset contains a large amount of measured signals involving different tool geometries under various operating conditions. The DBNMS is examined for both the tool state estimation and tool wear estimation tasks. In the experimental studies, the prediction results are evaluated and compared with popular machine learning approaches, which show the superior performance of the proposed DBNMS approach., Comment: 14 pages, 12 figures, 10 tables, submitted to IEEE Transactions on Cybernetics

While optimizing convex objective (loss) functions has been a powerhouse for machine learning for at least two decades, non-convex loss functions have attracted fast growing interests recently, due to many desirable properties such as superior robustness and classification accuracy, compared with their convex counterparts. The main obstacle for non-convex estimators is that it is in general intractable to find the optimal solution. In this paper, we study the computational issues for some non-convex M-estimators. In particular, we show that the stochastic variance reduction methods converge to the global optimal with linear rate, by exploiting the statistical property of the population loss. En route, we improve the convergence analysis for the batch gradient method in \cite{mei2016landscape}.

Although Recurrent Neural Network (RNN) has been a powerful tool for modeling sequential data, its performance is inadequate when processing sequences with multiple patterns. In this paper, we address this challenge by introducing a novel mixture layer and constructing an adaptive RNN. The mixture layer augmented RNN (termed as M-RNN) partitions patterns in training sequences into several clusters and stores the principle patterns as prototype vectors of components in a mixture model. By leveraging the mixture layer, the proposed method can adaptively update states according to the similarities between encoded inputs and prototype vectors, leading to a stronger capacity in assimilating sequences with multiple patterns. Moreover, our approach can be further extended by taking advantage of prior knowledge about data. Experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed method., Comment: 7 pages, 3 figures, 4 tables

We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded on game theory for understanding the aggregate effect of individual actions and predicting the temporal evolution of population distributions. We achieve a synthesis of MFG and Markov decision processes (MDP) by showing that a special MFG is reducible to an MDP. This enables us to broaden the scope of mean field game theory and infer MFG models of large real-world systems via deep inverse reinforcement learning. Our method learns both the reward function and forward dynamics of an MFG from real data, and we report the first empirical test of a mean field game model of a real-world social media population., Comment: Accepted to International Conference on Learning Representations (2018)