Fast Rates in α-Potential Games via Regularized Mirror Descent

An α-potential game is a multi-player non-cooperative interaction in which a global potential function approximates individual player rewards up to a structural bias α. 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 α-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 widetildeO(1/n) statistical rate, surpassing the standard widetildeO(1/√n) rate typical of offline multi-agent learning. This work characterizes the first fast-rate offline learning approach for α-potential games.