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Distributed projection subgradient algorithm for two-network zero-sum game with random sleep scheme

Control Theory and Technology 2021年第3期19卷 405-417页

作者： Hongyun Xiong Jiangxiong Han Xiaohong Nian Shiling Li School of Automation Central South UniversityChangsha410075China

In this paper,a zero-sum game Nash equilibrium computation problem with a common constraint set is investigated under two time-varying multi-agent subnetworks,where the two subnetworks have opposite payoff function.A novel distributed projection subgradient algorithm with random sleep scheme is developed to reduce the calculation amount of agents in the process of computing Nash *** our algorithm,each agent is determined by an independent identically distributed Bernoulli decision to compute the subgradient and perform the projection operation or to keep the previous consensus estimate,it effectively reduces the amount of computation and calculation ***,the traditional assumption of stepsize adopted in the existing methods is removed,and the stepsizes in our algorithm are randomized ***,we prove that all agents converge to Nash equilibrium with probability 1 by our ***,a simulation example verifies the validity of our algorithm.

关键词： Zero-sum game Nash equilibrium Time-varying multi-agent network projection subgradient algorithm Random sleep scheme

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Distributed projection subgradient algorithm Over Time-Varying General Unbalanced Directed Graphs

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2019年第3期64卷 1309-1316页

作者： Li, Huaqing Lu, Qingguo Huang, Tingwen Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China Texas A&M Univ Qatar Sci Program Doha 23874 Qatar

This paper is concerned with a general class of distributed constrained optimization problems over a multiagent network, where the global objective function is represented by the sum of all local objective functions. Each agent in the network only knows its own local objective function, and is restricted to a global nonempty closed convex set. We discuss the scenario where the communication of the whole multiagent network is expressed as a sequence of time-varying general unbalanced directed graphs. The directed graphs are required to be uniformly jointly strongly connected and the weight matrices are only rowstochastic. To collaboratively deal with the optimization problems, existing distributed methods mostly require the communication graph to be fixed or balanced, which is impractical and hardly inevitable. In contrast, we propose a new distributed projection subgradient algorithm which is applicable to the time-varying general unbalanced directed graphs and does not need each agent to knowits in-neighbors' out-degree. When the objective functions are convex and Lipschitz continuous, it is proved that the proposed algorithm exactly converges to the optimal solution. Simulation results on a numerical experiment are shown to substantiate feasibility of the proposed algorithm and correctness of the theoretical findings.

关键词： Distributed convex optimization multiagent network projection subgradient algorithm row-stochastic matrix time-varying unbalanced directed graphs

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Nash equilibrium computation of two-network zero-sum games with event-triggered communication

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Journal of Control and Decision 2022年第3期9卷 334-346页

作者： Hongyun Xiong Jiangxiong Han Xiaohong Nian Shiling Li School of Automation Central South UniversityChangshaPeople’s Republic of China

In this paper,a zero-sum game Nash equilibrium computation problem with event-triggered communication is investigated under an undirected weight-balanced multi-agent network.A novel distributed event-triggered projection subgradient algorithm is developed to reduce the communication burden within the *** the proposed algorithm,when the difference between the current state of the agent and the state of the last trigger time exceeds a given threshold,the agent will be triggered to communicate with its ***,we prove that all agents converge to Nash equilibrium by the proposed ***,two simulation examples verify that our algorithm not only reduces the communication burden but also ensures that the convergence speed and accuracy are close to that of the time-triggered method under the appropriate threshold.

关键词： Zero-sum game Nash equilibrium multi-agent network event-triggered communication projection subgradient algorithm

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