10,244 research outputs found

    Decentralized learning for wireless communications and networking

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    This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and recast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of parallelization. Without exchanging elements from the distributed training sets and keeping inter-node communications at affordable levels, the local (per-node) learners consent to the desired quantity inferred globally, meaning the one obtained if the entire training data set were centrally available. Impact of the decentralized learning framework to contemporary wireless communications and networking tasks is illustrated through case studies including target tracking using wireless sensor networks, unveiling Internet traffic anomalies, power system state estimation, as well as spectrum cartography for wireless cognitive radio networks.Comment: Contributed chapter to appear in Splitting Methods in Communication and Imaging, Science and Engineering, R. Glowinski, S. Osher, and W. Yin, Editors, New York, Springer, 201

    Stochastic Primal-Dual Algorithms with Faster Convergence than O(1/T)O(1/\sqrt{T}) for Problems without Bilinear Structure

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    Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main contribution of this paper is the design and analysis of new stochastic primal-dual algorithms that use a mixture of stochastic gradient updates and a logarithmic number of deterministic dual updates for solving a family of convex-concave problems with no bilinear structure assumed. Faster convergence rates than O(1/T)O(1/\sqrt{T}) with TT being the number of stochastic gradient updates are established under some mild conditions of involved functions on the primal and the dual variable. For example, for a family of problems that enjoy a weak strong convexity in terms of the primal variable and has a strongly concave function of the dual variable, the convergence rate of the proposed algorithm is O(1/T)O(1/T). We also investigate the effectiveness of the proposed algorithms for learning robust models and empirical AUC maximization

    Bandit Convex Optimization for Scalable and Dynamic IoT Management

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    The present paper deals with online convex optimization involving both time-varying loss functions, and time-varying constraints. The loss functions are not fully accessible to the learner, and instead only the function values (a.k.a. bandit feedback) are revealed at queried points. The constraints are revealed after making decisions, and can be instantaneously violated, yet they must be satisfied in the long term. This setting fits nicely the emerging online network tasks such as fog computing in the Internet-of-Things (IoT), where online decisions must flexibly adapt to the changing user preferences (loss functions), and the temporally unpredictable availability of resources (constraints). Tailored for such human-in-the-loop systems where the loss functions are hard to model, a family of bandit online saddle-point (BanSaP) schemes are developed, which adaptively adjust the online operations based on (possibly multiple) bandit feedback of the loss functions, and the changing environment. Performance here is assessed by: i) dynamic regret that generalizes the widely used static regret; and, ii) fit that captures the accumulated amount of constraint violations. Specifically, BanSaP is proved to simultaneously yield sub-linear dynamic regret and fit, provided that the best dynamic solutions vary slowly over time. Numerical tests in fog computation offloading tasks corroborate that our proposed BanSaP approach offers competitive performance relative to existing approaches that are based on gradient feedback

    Information based approach to stochastic control problems

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    An information based method for solving stochastic control problems with partial observation has been proposed. First, the information-theoretic lower bounds of the cost function has been analysed. It has been shown, under rather weak assumptions, that reduction of the expected cost with closed-loop control compared to the best open-loop strategy is upper bounded by non-decreasing function of mutual information between control variables and the state trajectory. On the basis of this result, an Information Based Control method has been developed. The main idea of the IBC consists in replacing the original control task by a sequence of control problems that are relatively easy to solve and such that information about the state of the system is actively generated. Two examples of the operation of the IBC are given. It has been shown that the IBC is able to find the optimal solution without using dynamic programming at least in these examples. Hence the computational complexity of the IBC is substantially smaller than complexity of dynamic programming, which is the main advantage of the proposed method.Comment: This is a preprint of an article accepted for publication in International Journal of Applied Mathematics and Computer Science, AMCS, 20 pages, 1 figur

    Reinforcement Learning: Stochastic Approximation Algorithms for Markov Decision Processes

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    This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov decision processes

    Adaptive Newton Method for Empirical Risk Minimization to Statistical Accuracy

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    We consider empirical risk minimization for large-scale datasets. We introduce Ada Newton as an adaptive algorithm that uses Newton's method with adaptive sample sizes. The main idea of Ada Newton is to increase the size of the training set by a factor larger than one in a way that the minimization variable for the current training set is in the local neighborhood of the optimal argument of the next training set. This allows to exploit the quadratic convergence property of Newton's method and reach the statistical accuracy of each training set with only one iteration of Newton's method. We show theoretically and empirically that Ada Newton can double the size of the training set in each iteration to achieve the statistical accuracy of the full training set with about two passes over the dataset

    Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset

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    Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal Component Analysis (RPCA) solved via Principal Component Pursuit (PCP) which decomposes a data matrix in a low-rank matrix and a sparse matrix. However, similar robust implicit or explicit decompositions can be made in the following problem formulations: Robust Non-negative Matrix Factorization (RNMF), Robust Matrix Completion (RMC), Robust Subspace Recovery (RSR), Robust Subspace Tracking (RST) and Robust Low-Rank Minimization (RLRM). The main goal of these similar problem formulations is to obtain explicitly or implicitly a decomposition into low-rank matrix plus additive matrices. In this context, this work aims to initiate a rigorous and comprehensive review of the similar problem formulations in robust subspace learning and tracking based on decomposition into low-rank plus additive matrices for testing and ranking existing algorithms for background/foreground separation. For this, we first provide a preliminary review of the recent developments in the different problem formulations which allows us to define a unified view that we called Decomposition into Low-rank plus Additive Matrices (DLAM). Then, we examine carefully each method in each robust subspace learning/tracking frameworks with their decomposition, their loss functions, their optimization problem and their solvers. Furthermore, we investigate if incremental algorithms and real-time implementations can be achieved for background/foreground separation. Finally, experimental results on a large-scale dataset called Background Models Challenge (BMC 2012) show the comparative performance of 32 different robust subspace learning/tracking methods.Comment: 121 pages, 5 figures, submitted to Computer Science Review. arXiv admin note: text overlap with arXiv:1312.7167, arXiv:1109.6297, arXiv:1207.3438, arXiv:1105.2126, arXiv:1404.7592, arXiv:1210.0805, arXiv:1403.8067 by other authors, Computer Science Review, November 201

    Scaling-up Distributed Processing of Data Streams for Machine Learning

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    Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these applications. Further, these applications often involve data that are either inherently gathered at geographically distributed entities or that are intentionally distributed across multiple machines for memory, computational, and/or privacy reasons. Training of models in this distributed, streaming setting requires solving stochastic optimization problems in a collaborative manner over communication links between the physical entities. When the streaming data rate is high compared to the processing capabilities of compute nodes and/or the rate of the communications links, this poses a challenging question: how can one best leverage the incoming data for distributed training under constraints on computing capabilities and/or communications rate? A large body of research has emerged in recent decades to tackle this and related problems. This paper reviews recently developed methods that focus on large-scale distributed stochastic optimization in the compute- and bandwidth-limited regime, with an emphasis on convergence analysis that explicitly accounts for the mismatch between computation, communication and streaming rates. In particular, it focuses on methods that solve: (i) distributed stochastic convex problems, and (ii) distributed principal component analysis, which is a nonconvex problem with geometric structure that permits global convergence. For such methods, the paper discusses recent advances in terms of distributed algorithmic designs when faced with high-rate streaming data. Further, it reviews guarantees underlying these methods, which show there exist regimes in which systems can learn from distributed, streaming data at order-optimal rates.Comment: 45 pages, 9 figures; preprint of a journal paper published in Proceedings of the IEEE (Special Issue on Optimization for Data-driven Learning and Control

    Low-complexity modeling of partially available second-order statistics: theory and an efficient matrix completion algorithm

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    State statistics of linear systems satisfy certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. In the present paper we study the problem of completing partially known state statistics. Our aim is to develop tools that can be used in the context of control-oriented modeling of large-scale dynamical systems. For the type of applications we have in mind, the dynamical interaction between state variables is known while the directionality and dynamics of input excitation is often uncertain. Thus, the goal of the mathematical problem that we formulate is to identify the dynamics and directionality of input excitation in order to explain and complete observed sample statistics. More specifically, we seek to explain correlation data with the least number of possible input disturbance channels. We formulate this inverse problem as rank minimization, and for its solution, we employ a convex relaxation based on the nuclear norm. The resulting optimization problem is cast as a semidefinite program and can be solved using general-purpose solvers. For problem sizes that these solvers cannot handle, we develop a customized alternating minimization algorithm (AMA). We interpret AMA as a proximal gradient for the dual problem and prove sub-linear convergence for the algorithm with fixed step-size. We conclude with an example that illustrates the utility of our modeling and optimization framework and draw contrast between AMA and the commonly used alternating direction method of multipliers (ADMM) algorithm.Comment: Submitted to IEEE Transactions on Automatic Contro

    Asynchronous Decentralized Stochastic Optimization in Heterogeneous Networks

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    We consider expected risk minimization in multi-agent systems comprised of distinct subsets of agents operating without a common time-scale. Each individual in the network is charged with minimizing the global objective function, which is an average of sum of the statistical average loss function of each agent in the network. Since agents are not assumed to observe data from identical distributions, the hypothesis that all agents seek a common action is violated, and thus the hypothesis upon which consensus constraints are formulated is violated. Thus, we consider nonlinear network proximity constraints which incentivize nearby nodes to make decisions which are close to one another but not necessarily coincide. Moreover, agents are not assumed to receive their sequentially arriving observations on a common time index, and thus seek to learn in an asynchronous manner. An asynchronous stochastic variant of the Arrow-Hurwicz saddle point method is proposed to solve this problem which operates by alternating primal stochastic descent steps and Lagrange multiplier updates which penalize the discrepancies between agents. This tool leads to an implementation that allows for each agent to operate asynchronously with local information only and message passing with neighbors. Our main result establishes that the proposed method yields convergence in expectation both in terms of the primal sub-optimality and constraint violation to radii of sizes O(T)\mathcal{O}(\sqrt{T}) and O(T3/4)\mathcal{O}(T^{3/4}), respectively. Empirical evaluation on an asynchronously operating wireless network that manages user channel interference through an adaptive communications pricing mechanism demonstrates that our theoretical results translates well to practice
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