Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability

Researchers achieve the first fast statistical rates (Õ(ε⁻¹)) for offline contextual bandits using forward-KL regularization under single-policy concentrability, matching the performance previously only shown for reverse-KL approaches and establishing rate-optimal lower bounds.

This paper advances the theoretical foundations of reinforcement learning by resolving a significant gap in the analysis of forward-KL-regularized offline decision-making algorithms. While reverse-KL regularization had demonstrated fast Õ(ε⁻¹) sample complexity rates, forward-KL approaches remained stuck at slower Õ(ε⁻²) rates despite their practical prevalence in real-world systems. The authors establish the first matching fast rates for forward-KL regularization, suggesting these methods are computationally equivalent to their reverse-KL counterparts from a statistical perspective.

The breakthrough stems from a novel analytical framework that leverages the pessimism principle through convex optimization techniques, bypassing traditional mean value theorem approaches used in prior work. This methodological contribution extends across both tabular and function approximation settings under single-policy concentrability assumptions, demonstrating the generality of their approach. The authors additionally provide rate-optimal lower bounds proving their upper bounds cannot be improved, establishing theoretical tightness.

For the broader reinforcement learning and AI optimization community, this work validates the theoretical soundness of forward-KL-regularized objectives widely used in practice. The streamlined proof techniques may enable faster progress on related problems in offline RL and contextual bandits. However, the practical implications remain limited since this addresses sample complexity rather than computational efficiency or convergence guarantees. The results primarily benefit researchers developing RL theory and practitioners seeking theoretical justification for existing algorithm choices.

• →First Õ(ε⁻¹) fast rates achieved for forward-KL regularized offline contextual bandits, matching reverse-KL performance
• →Novel convex-analytical framework provides rate-optimal upper and lower bounds under single-policy concentrability
• →Forward-KL sample complexity recovers unregularized slow rates in low-regularization regime, mirroring reverse-KL behavior
• →Streamlined proof techniques using pessimism principle may accelerate progress on related offline RL problems
• →Results extend across tabular and function approximation settings, demonstrating broad applicability