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

Journal article (2021)

Authors

B. Franci Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
S. Grammatico Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2021 B. Franci, S. Grammatico
DOI: https://doi.org/10.1109/TAC.2020.3047369
Cost function Convergence Uncertainty Approximation algorithms Stochastic processes Nash equilibrium Random variables Stochastic approximation Stochastic generalized Nash equilibrium problems Variational inequalities
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Published Date

2021

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.