Beyond Pessimism: Offline Learning in KL-regularized Games

Offline multi-agent reinforcement learning in general-sum settings is challenged by the distribution shift between logged datasets and target equilibrium policies. While standard methods rely on manual pessimistic penalties, we demonstrate that KL regularization suffices to stabilize learning and achieve equilibrium recovery. We propose General-sum Anchored Nash Equilibrium (GANE), which recovers regularized Nash equilibria at an accelerated statistical rate of $\widetilde{O}(1/n)$. For computational tractability, we develop General-sum Anchored Mirror Descent (GAMD), an iterative algorithm converging to a Coarse Correlated Equilibrium at the standard rate of $\widetilde{O}(1/\sqrt{n}+1/T)$. These results establish KL regularization as a standalone mechanism for pessimism-free offline learning that achieves equivalent or accelerated rates in multi-player general-sum games.

We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to stabilize learning and guarantee convergence. We first introduce Regularized Offline Sequential Equilibrium (ROSE), a theoretical framework that achieves a fast $\widetilde{\mathcal{O}}(1/n)$ convergence rate under unilateral concentrability, improving over the standard $\widetilde{\mathcal{O}}(1/\sqrt{n})$ rates in unregularized settings. We then propose Sequential Offline Self-play Mirror Descent (SOS-MD), a practical model-free algorithm based on least-squares value estimation and iterative self-play updates. We prove that the last iterate of SOS-MD attains the same $\widetilde{\mathcal{O}}(1/n)$ statistical rate up to a vanishing optimization error of order $\widetilde{\mathcal{O}}(1/\sqrt{T})$ in the number of self-play iterations $T$.

This paper investigates offline Q-learning for finite-horizon Markov decision processes with Kullback-Leibler (KL) regularization. Recent studies have shown that KL regularization can yield fast rates in offline decision-making problems. However, it remains unclear whether Q-learning, which adopts incremental stochastic approximation updates, can achieve such fast rates in the offline setting. We first propose KL-regularized Q-Learning (KLQ), a simple variant of classical Q-learning. By exploiting KL regularization, we prove that KLQ achieves a sample complexity of $\widetilde{O}(1/ε)$ without explicit pessimism. This guarantee, however, has an exponential dependence on the KL regularization parameter and the horizon. To address this limitation, we further propose KL-regularized Pessimistic Q-Learning (KLPQ), which incorporates pessimism into KLQ. We prove that KLPQ retains the same $\widetilde O(1/ε)$ rate while removing the explicit exponential dependence, thereby further improving the sample complexity. To the best of our knowledge, these results establish the first fast-rate guarantees for offline Q-learning in tabular finite-horizon KL-regularized MDPs.