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.

References in corpus (5)

• A distributed primal-dual algorithm for computation of generalized Nash equilibria with shared affine coupling constraints via operator splitting methods
• Dynamic control of agents playing aggregative games with coupling constraints
• Distributed Learning for Stochastic Generalized Nash Equilibrium Problems
• Forward-backward-forward methods with variance reduction for stochastic variational inequalities
• Distributed forward-backward (half) forward algorithms for generalized Nash equilibrium seeking