Fast Rates in $\alpha$-Potential Games via Regularized Mirror Descent

TL;DR

This paper introduces a novel offline learning algorithm for $oldsymbol{ extit{ extalpha}}$-potential games that achieves fast convergence rates by leveraging a new data coverage framework and regularized mirror descent.

Contribution

It proposes Offline Potential Mirror Descent (OPMD), the first fast-rate offline learning method for $ extalpha$-potential games, with a verifiable data coverage condition.

Findings

Achieves an accelerated $ ilde{O}(1/n)$ statistical rate.

Introduces a Reference-Anchored offline data coverage framework.

Surpasses the standard $ ilde{O}(1/ oot{2} )$ rate in offline multi-agent learning.

Abstract

An $\alpha$-potential game is a multi-player non-cooperative interaction in which a global potential function approximates individual player rewards up to a structural bias $\alpha$. While identifying a Nash Equilibrium (NE) in generic general-sum games is known to be computationally intractable, the potential game structure enables tractable NE identification. In this paper, we study the offline learning of NE in $\alpha$-potential games using KL regularization. To analyze this process, we propose a novel Reference-Anchored offline data coverage framework--a verifiable condition that anchors data requirements to a known reference policy rather than an unknown optimum. Building on this, we propose Offline Potential Mirror Descent (OPMD), a decentralized algorithm that achieves an accelerated $\widetilde{\mathcal{O}}(1/n)$ statistical rate, surpassing the standard $\widetilde{\mathcal{O}}(1/\sqrt{n})$ rate typical of offline multi-agent learning. This work characterizes the first fast-rate offline learning approach for $\alpha$-potential games.