Stochastic generalized Nash equilibrium seeking under partial-decision information

TL;DR

This paper introduces stochastic generalized Nash equilibrium algorithms for network and aggregative games with partial information, proving convergence using a preconditioned forward-backward splitting method and variance reduction techniques.

Contribution

It is the first to address stochastic GNE problems with partial-decision information and provides distributed algorithms with convergence guarantees.

Findings

Algorithms converge to GNE under certain conditions.

Use of variance reduction improves estimation accuracy.

Applicable to network and aggregative games.

Abstract

We consider for the first time a stochastic generalized Nash equilibrium problem, i.e., with expected-value cost functions and joint feasibility constraints, under partial-decision information, meaning that the agents communicate only with some trusted neighbours. We propose several distributed algorithms for network games and aggregative games that we show being special instances of a preconditioned forward-backward splitting method. We prove that the algorithms converge to a generalized Nash equilibrium when the forward operator is restricted cocoercive by using the stochastic approximation scheme with variance reduction to estimate the expected value of the pseudogradient.