Distributed Forward-Backward algorithms for stochastic generalized Nash equilibrium seeking
Abstract
We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEP, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. As main contribution, we show almost sure convergence of our proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive. For non-generalized SNEPs, we show almost sure convergence also if the pseudogradient mapping is restricted strictly monotone. Numerical simulations show that the proposed forward-backward algorithm seems faster that other available algorithms.
Cite
@article{arxiv.1912.04165,
title = {Distributed Forward-Backward algorithms for stochastic generalized Nash equilibrium seeking},
author = {Barbara Franci and Sergio Grammatico},
journal= {arXiv preprint arXiv:1912.04165},
year = {2020}
}