• Home
  • Uncategorized
  • On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization

arXiv:2605.02141v1 Announce Type: cross
Abstract: Kullback-Leibler (KL) regularization is widely used in offline decision-making and offers several benefits, motivating recent work on the sample complexity of offline learning with respect to KL-regularized performance metrics. Nevertheless, the exact sample complexity of KL-regularized offline learning remains largely from fully characterized. In this paper, we study this question in the setting of multi-armed bandits (MABs). We provide a sharp analysis of KL-PCB (Zhao et al., 2026), showing that it achieves a sample complexity of $tildeO(eta SAC^pi^*/epsilon)$ under large regularization $eta = tildeO(epsilon^-1)$, and a sample complexity of $tildeOmega(SAC^pi^*/epsilon^2)$ under small regularization $eta = tildeOmega(epsilon^-1)$, where $eta$ is the regularization parameter, $S$ is the number of contexts, $A$ is the number of arms, $C^pi^*$ policy coverage coefficient at the optimal policy $pi^*$, $epsilon$ is the desired sub-optimality, and $tildeO$ and $tildeOmega$ hide all poly-logarithmic factors. We further provide a pair of sharper sample complexity lower bounds, which matches the upper bounds over the entire range of regularization strengths. Overall, our results provide a nearly complete characterization of offline multi-armed bandits with KL regularization.

Subscribe for Updates

Copyright 2025 dijee Intelligence Ltd.   dijee Intelligence Ltd. is a private limited company registered in England and Wales at Media House, Sopers Road, Cuffley, Hertfordshire, EN6 4RY, UK registration number 16808844