Convergence Rate of Generalized Nash Equilibrium Learning in Strongly Monotone Games with Linear Constraints

TL;DR

This paper analyzes the convergence rate of payoff-based learning algorithms for generalized Nash equilibria in strongly monotone games with linear constraints, introducing a novel regularization technique.

Contribution

It provides the first characterization of the convergence speed of iterates to a variational GNE in such structured games using payoff-based feedback.

Findings

Established convergence rates under one-point feedback

Established convergence rates under two-point feedback

Introduced a partial regularization technique for GNE learning

Abstract

We consider payoff-based learning of a generalized Nash equilibrium (GNE) in multi-agent systems. Our focus is on games with jointly convex constraints of a linear structure and strongly monotone pseudo-gradients. We present a convergent procedure based on a partial regularization technique and establish the convergence rate of its iterates under one- and two-point payoff-based feedback. To the best of our knowledge, this work is the first one characterizing the convergence speed of iterates to a variational GNE in the class of games under consideration.