Convergence Rate of Payoff-based Generalized Nash Equilibrium Learning

TL;DR

This paper establishes the convergence rate of a payoff-based learning algorithm for generalized Nash equilibrium problems with strongly monotone pseudo-gradients and linear constraints, filling a gap in understanding its efficiency.

Contribution

It provides the first known convergence rate for payoff-based algorithms in this class of GNE problems, using a novel game extension approach.

Findings

Convergence rate of O(1/t^{4/7}) to a variational GNE.

Applicable to games with strongly monotone pseudo-gradients.

Addresses an open problem in payoff-based convergence analysis.

Abstract

We consider generalized Nash equilibrium (GNE) problems in games with strongly monotone pseudo-gradients and jointly linear coupling constraints. We establish the convergence rate of a payoff-based approach intended to learn a variational GNE (v-GNE) in such games. While convergent algorithms have recently been proposed in this setting given full or partial information of the gradients, rate of convergence in the payoff-based information setting has been an open problem. Leveraging properties of a game extended from the original one by a dual player, we establish a convergence rate of $O(\frac{1}{t^{4/7}})$ to a v-GNE of the game.