Fast Offline Equilibrium Learning in $\alpha$-Potential Games

An $\alpha$-potential game is a multi-player non-cooperative interaction in which a global potential function tracks individual player incentives 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 provides a scalar objective whose approximate maximizers yield approximate equilibria. 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 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 $\tilde{\mathcal{O}}(1/n)$ statistical rate for the regularized game, compared with the $\tilde{\mathcal{O}}(1/\sqrt{n})$ rate typical of unregularized offline multi-agent learning. To our knowledge, this work characterizes the first fast-rate offline learning approach for $\alpha$-potential games.