Forward-Backward algorithms for stochastic Nash equilibrium seeking in restricted strongly and strictly monotone games

TL;DR

This paper introduces a forward-backward algorithm for stochastic Nash equilibrium problems with restricted monotonicity, proving convergence under various conditions and demonstrating potential speed advantages over existing methods.

Contribution

It develops a novel forward-backward algorithm tailored for restricted monotone stochastic Nash problems and establishes its convergence properties.

Findings

Algorithm converges under restricted strong and strict monotonicity.

Numerical results indicate faster convergence compared to existing algorithms.

Approximates expected values using sampling strategies.

Abstract

We study stochastic Nash equilibrium problems with expected valued cost functions whose pseudogradient satisfies restricted monotonicity properties which hold only with respect to the solution. We propose a forward-backward algorithm and prove its convergence under restricted strong monotonicity, restricted strict monotonicity and restricted cocoercivity of the pseudogradient mapping. To approximate the expected value, we use either a finite number of samples and a vanishing step size or an increasing number of samples with a constant step. Numerical simulations show that our proposed algorithm might be faster than the available algorithms.