A Fast Convergence Theory for Offline Decision Making

Abstract: This paper proposes the first generic fast convergence result in general function approximation for offline decision making problems, which include offline reinforcement learning (RL) and off-policy evaluation (OPE) as special cases. To unify different settings, we introduce a framework called Decision Making with Offline Feedback (DMOF), which captures a wide range of offline decision making problems. Within this framework, we propose a simple yet powerful algorithm called Empirical Decision with Divergence (EDD), whose upper bound can be termed as a coefficient named Empirical Offline Estimation Coefficient (EOEC). We show that EOEC is instance-dependent and actually measures the correlation of the problem. When assuming partial coverage in the dataset, EOEC will reduce in a rate of $1/N$ where $N$ is the size of the dataset, endowing EDD with a fast convergence guarantee. Finally, we complement the above results with a lower bound in the DMOF framework, which further demonstrates the soundness of our theory.