BATCH POLICY LEARNING IN AVERAGE REWARD MARKOV DECISION PROCESSES

• 成果类型: Article
• 署名作者: Liao, Peng; Qi, Zhengling; Wan, Runzhe; Klasnja, Predrag; Murphy, Susan A.
• 署名单位: Harvard University; George Washington University; Amazon.com; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2231
• 发表日期: 2022
• 页码: 3364-3387
• 关键词: dynamic treatment regimes; algorithms; trials; DESIGN

摘要

We consider the batch (off-line) policy learning problem in the infinite horizon Markov decision process. Motivated by mobile health applications, we focus on learning a policy that maximizes the long-term average reward. We propose a doubly robust estimator for the average reward and show that it achieves semiparametric efficiency. Further, we develop an optimization algorithm to compute the optimal policy in a parameterized stochastic policy class. The performance of the estimated policy is measured by the difference between the optimal average reward in the policy class and the average reward of the estimated policy and we establish a finite-sample regret guarantee. The performance of the method is illustrated by simulation studies and an analysis of a mobile health study promoting physical activity.