Projected State-action Balancing Weights for Offline Reinforcement Learning

Abstract

Offline policy evaluation (OPE) is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on the value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with approximately projected state-action balancing weights for the policy value estimation. We obtain the convergence rate of these weights and show that the proposed value estimator is semi-parametric efficient under technical conditions. In terms of asymptotics, our results scale with both the number of trajectories and the number of decision points at each trajectory. As such, consistency can still be achieved with a limited number of subjects when the number of decision points diverges. In addition, we develop a necessary and sufficient condition for establishing the well-posedness of the Bellman operator in the off-policy setting, which characterizes the difficulty of OPE and may be of independent interest. Numerical experiments demonstrate the promising performance of our proposed estimator.

References in corpus (6)

• Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
• Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions
• Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations
• Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes
• Large sample analysis of the median heuristic
• Statistical Inference of the Value Function for Reinforcement Learning in Infinite Horizon Settings