# Fast Rates in α-Potential Games via Regularized Mirror Descent

arXiv: https://arxiv.org/abs/2605.00268 · HTML: https://mlsanity.com/paper/2605.00268/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2026.

## Built on by (most cited first, 5 of 5)

- [Offline Two-Player Zero-Sum Markov Games with KL Regularization](https://mlsanity.com/paper/2605.13025/) (2026)
- [Robust Data-Collection Policy Learning for Low-Variance Online Policy Evaluation](https://mlsanity.com/paper/2608.24146/) (2026)
- [OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items](https://mlsanity.com/paper/2609.01933/) (2026)
- [Pessimistic Minimax Learning for Public-Private Information Games under Unilateral Coverage](https://mlsanity.com/paper/2610.04997/) (2026)
- [Fast Rates for Offline Q-Learning with KL Regularization](https://mlsanity.com/paper/2610.18839/) (2026)

## Abstract (arXiv)

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.