Statistical inference of the value function for reinforcement learning in infinite‐horizon settings. (22nd December 2021)

• Record Type: Journal Article
• Authors: Shi, Chengchun; Zhang, Sheng; Lu, Wenbin; Song, Rui
• Is Part Of: Journal of the Royal Statistical Society. Volume 84:Number 3(2022)
• Page Start: 765
• Page End: 793
• Publication Date: 2021-12-22
• Subjects: bidirectional asymptotics -- confidence interval -- infinite horizons -- reinforcement learning -- value function; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12465
• Languages: English
• ISSNs: 1369-7412

Abstract

Abstract: Reinforcement learning is a general technique that allows an agent to learn an optimal policy and interact with an environment in sequential decision‐making problems. The goodness of a policy is measured by its value function starting from some initial state. The focus of this paper was to construct confidence intervals (CIs) for a policy's value in infinite horizon settings where the number of decision points diverges to infinity. We propose to model the action‐value state function (Q‐function) associated with a policy based on series/sieve method to derive its confidence interval. When the target policy depends on the observed data as well, we propose a S equentiA l V alue E valuation (SAVE) method to recursively update the estimated policy and its value estimator. As long as either the number of trajectories or the number of decision points diverges to infinity, we show that the proposed CI achieves nominal coverage even in cases where the optimal policy is not unique. Simulation studies are conducted to back up our theoretical findings. We apply the proposed method to a dataset from mobile health studies and find that reinforcement learning algorithms could help improve patient's health status. A Python implementation of the proposed procedure is available at https://github.com/shengzhang37/SAVE .