An Online Feasible Point Method for Benign Generalized Nash Equilibrium Problems

TL;DR

This paper introduces an online feasible point method for generalized Nash equilibrium problems that guarantees feasibility at every iteration and converges to equilibrium in benign cases, addressing a key challenge in multi-agent online learning with time-varying constraints.

Contribution

The paper proposes a novel online feasible point method that ensures feasibility at all times and converges to a generalized Nash equilibrium for a specific class of benign problems.

Findings

Guarantees feasibility at each iteration.

Converges to equilibrium in benign cases.

Applicable with limited communication between agents.

Abstract

We consider a repeatedly played generalized Nash equilibrium game. This induces a multi-agent online learning problem with joint constraints. An important challenge in this setting is that the feasible set for each agent depends on the simultaneous moves of the other agents and, therefore, varies over time. As a consequence, the agents face time-varying constraints, which are not adversarial but rather endogenous to the system. Prior work in this setting focused on convergence to a feasible solution in the limit via integrating the constraints in the objective as a penalty function. However, no existing work can guarantee that the constraints are satisfied for all iterations while simultaneously guaranteeing convergence to a generalized Nash equilibrium. This is a problem of fundamental theoretical interest and practical relevance. In this work, we introduce a new online feasible point method. Under the assumption that limited communication between the agents is allowed, this method guarantees feasibility. We identify the class of benign generalized Nash equilibrium problems, for which the convergence of our method to the equilibrium is guaranteed. We set this class of benign generalized Nash equilibrium games in context with existing definitions and illustrate our method with examples.