Asynchronous distributed algorithms for seeking generalized Nash equilibria under full and partial decision information

TL;DR

This paper develops asynchronous distributed algorithms for finding generalized Nash equilibria in multi-agent networks, handling full and partial decision information scenarios with convergence guarantees and numerical validation.

Contribution

It introduces novel asynchronous algorithms for generalized Nash equilibrium seeking that operate without centralized coordination, accommodating delayed and partial information.

Findings

Algorithms converge under proper assumptions and step sizes.

Numerical studies confirm convergence and efficiency.

Algorithms remove idle time and exploit local computation resources.

Abstract

We investigate asynchronous distributed algorithms with delayed information for seeking generalized Nash equilibrium over multi-agent networks. The considered game model has all players' local decisions coupled with a shared affine constraint. We assume each player can only access its local objective function, local constraint, and a local block matrix of the affine constraint. We first give the algorithm for the case when each agent is able to fully access all other players' decisions. With the help of auxiliary edge variables and edge Laplacian matrix, each player can carry on its local iteration in an asynchronous manner, using only local data and possibly delayed neighbour information. And then we investigate the case when the agents cannot know all other players' decisions, which is called a partial decision case. We introduce a local estimation of the overall decisions for each agent in the partial decision case, and develop another asynchronous algorithm by incorporating consensus dynamics on the local estimations of the overall decisions. Since both algorithms do not need any centralized clock coordination, the algorithms fully exploit the local computation resource of each player, and remove the idle time due to waiting for the "slowest" agent. Both algorithms are developed by a preconditioned forward-backward operator splitting method, while convergence is shown with the help of asynchronous fixed-point iterations under proper assumptions and fixed step-size choices. Numerical studies verify both algorithms' convergence and efficiency.