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Distributed quantized mirror descent for strongly convex optimization over time-varying directed graph

Science China(Information Sciences) 2022年第10期65卷 196-210页

作者： Menghui XIONG Baoyong ZHANG Deming YUAN Shengyuan XU School of Automation Nanjing University of Science and Technology

This paper investigates a distributed strongly convex constrained optimization problem in the non-Euclidean sense, where the bit rate of the considered communication between nodes is assumed to be limited, and the communication topology is represented by a time-varying directed graph. By considering the limitation of communication capacity, the quantization technique is applied in the process of exchanging information over the network. Then a distributed quantized mirror descent(DQMD) algorithm, which uses the Bregman divergence and time-varying quantizers, is developed for the strongly convex optimization under a convex constraint set. The convergence of the developed algorithm is also analyzed. It is shown that the nodes' state errors are bounded by some terms related to the quantization resolutions, and the sublinear upper-bounds can be guaranteed by choosing appropriate quantization resolutions. Finally, a distributed ridge regression is provided as an example to verify the validity of the proposed method.

关键词： distributed convex optimization strongly convex optimization mirror descent quantized communication Bregman divergence

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Distributed stochastic mirror descent algorithm for resource allocation problem

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Control Theory and Technology 2020年第4期18卷 339-347页

作者： Yinghui Wang Zhipeng Tu Huashu Qin Key Lab of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100190China

In this paper,we consider a distributed resource allocation problem of minimizing a global convex function formed by a sum of local convex functions with coupling *** on neighbor communication and stochastic gradient,a distributed stochastic mirror descent algorithm is designed for the distributed resource allocation *** convergence to an optimal solution of the proposed algorithm is given when the second moments of the gradient noises are summable.A numerical example is also given to illustrate the effectiveness of the proposed algorithm.

关键词： Distributed Resource allocation problem Stochastic gradient mirror descent

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An Accelerated Stochastic mirror descent Method

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Journal of the Operations Research Society of China 2024年第3期12卷 549-571页

作者： Bo-Ou Jiang Ya-Xiang Yuan LSEC ICMSECAMSSChinese Academy of SciencesBeijing100190China Department of Mathematics University of Chinese Academy of SciencesBeijing100049China

Driven by large-scale optimization problems arising from machine learning,the development of stochastic optimization methods has witnessed a huge *** types of methods have been developed based on vanilla stochastic gradient descent ***,for most algorithms,convergence rate in stochastic setting cannot simply match that in deterministic *** understanding the gap between deterministic and stochastic optimization is the main goal of this ***,we are interested in Nesterov acceleration of gradient-based *** our study,we focus on acceleration of stochastic mirror descent method with implicit regularization *** that the problem objective is smooth and convex or strongly convex,our analysis prescribes the method parameters which ensure fast convergence of the estimation error and satisfied numerical performance.

关键词： Large-scale optimization Variance reduction mirror descent Acceleration Independent sampling Importance sampling

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Distributed No-Regret Learning for Stochastic Aggregative Games over Networks

Distributed No-Regret Learning for Stochastic Aggregative Ga...

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第40届中国控制会议

作者： Jinlong Lei Peng Yi Li Li The Department of Control Science and Engineering Tongji University The Institute for Advanced Study Tongji University Shanghai Research Institute for Intelligent Autonomous Systems

In this work, we propose a distributed no-regret learning for stochastic aggregative games over time-varying *** consider a finite set of players repeatedly playing the network aggregative game in stochastic regimes, where each player has an expectation-valued objective function depending on its own strategy and the aggregate of all player strategies, and the players can estimate gradients of their objective functions up to a zero-mean error with bounded variance. We consider the scenario in which players cannot directly obtain the aggregate value, but they are able to share their estimates of the aggregate with their neighbors without disclosing their own strategies. We design a distributed learning algorithm based on the mirror descent and dynamical averaging tracking. We then provide analysis for both the variational regret and the cost r√egret for aggregative games These analyses indicate the key correlations between the regret bounds, the network connectivity, and game structures, etc. In addition, we validate the almost sure convergence to the Nash equilibrium for the class of strictly monotone games. Finally, we present preliminary numerics by applying the proposed scheme to the Nash-Cournot competition problem.

关键词： Network Aggregative Games Distributed Learning No-regret Learning mirror descent

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