# Distributed Forward-Backward algorithms for stochastic generalized Nash equilibrium seeking

arXiv: https://arxiv.org/abs/1912.04165 · HTML: https://mlsanity.com/paper/1912.04165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Finite-sample guarantees for data-driven forward-backward operator methods](https://mlsanity.com/paper/2512.19172/) (2025)
- [Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach](https://mlsanity.com/paper/2511.14048/) (2025)

## Abstract (arXiv)

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.