A Distributed Forward-Backward Algorithm for Stochastic Generalized Nash Equilibrium Seeking

• 成果类型: Article
• 署名作者: Franci, Barbara; Grammatico, Sergio
• 署名单位: Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047369
• 发表日期: 2021
• 页码: 5467-5473
• 关键词: Cost function; Stochastic processes; Random variables; Nash equilibrium; uncertainty; CONVERGENCE; Approximation algorithms; stochastic approximation; stochastic generalized Nash equilibrium problems (SGNEPs); Variational inequalities

摘要

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.