A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking

TL;DR

This paper introduces a distributed algorithm for solving stochastic generalized Nash equilibrium problems, leveraging forward-backward splitting and proving almost sure convergence as sample size increases.

Contribution

It proposes a novel damped forward-backward algorithm for stochastic GNEPs with convergence guarantees, inspired by prior work but adapted for stochastic settings.

Findings

Algorithm converges almost surely with increasing sample size.

Effective for distributed stochastic GNEPs with expected-value costs.

Provides theoretical convergence proof under specified conditions.

Abstract

We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward-backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.