Distributed forward-backward (half) forward algorithms for generalized Nash equilibrium seeking

TL;DR

This paper introduces two novel distributed algorithms for finding generalized Nash equilibria in monotone games, utilizing operator splitting techniques, and compares their performance through numerical experiments.

Contribution

The paper proposes two new distributed algorithms based on forward-backward-forward and forward-backward-half-forward operator splitting methods for generalized Nash equilibrium seeking.

Findings

The algorithms successfully compute Nash equilibria in monotone games.

Numerical experiments demonstrate the effectiveness and comparison of the proposed methods.

The second algorithm requires the pseudo-gradient to be cocoercive.

Abstract

We present two distributed algorithms for the computation of a generalized Nash equilibrium in monotone games. The first algorithm follows from a forward-backward-forward operator splitting, while the second, which requires the pseudo-gradient mapping of the game to be cocoercive, follows from the forward-backward-half-forward operator splitting. Finally, we compare them with the distributed, preconditioned, forward-backward algorithm via numerical experiments.