Stochastic Generalized Nash Equilibrium-Seeking in Merely Monotone Games

• 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.2021.3108496
• 发表日期: 2022
• 页码: 3905-3919
• 关键词: Cost function; Nash equilibrium; games; Stochastic processes; Random variables; Couplings; CONVERGENCE; Stochastic generalized Nash equilibrium problems; stochastic variational inequalities

摘要

We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE-seeking algorithm for monotone games that require one proximal computation (e.g., one projection step) and one pseudogradient evaluation per iteration. Our main contribution is to extend the relaxed forward-backward operator splitting by the Malitsky (Mathematical Programming, 2019) to the stochastic case and in turn to show almost sure convergence to an SGNE when the expected value of the pseudogradient is approximated by the average over a number of random samples.