Library Header Image
LSE Research Online LSE Library Services

Statistical inference of the value function for reinforcement learning in infinite-horizon settings

Shi, Chengchun, Zhang, Shengxing, Lu, Wenbin and Song, Rui (2021) Statistical inference of the value function for reinforcement learning in infinite-horizon settings. Journal of the Royal Statistical Society. Series B: Statistical Methodology. ISSN 1369-7412 (In Press)

[img] Text (Statistical Inference of the Value Function for Reinforcement Learning in Infinite-Horizon Settings) - Accepted Version
Pending embargo until 1 January 2100.

Download (4MB) | Request a copy


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 is 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 SequentiAl Value Evaluation (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

Item Type: Article
Official URL:
Additional Information: © 2021 Royal Statistical Society
Divisions: Statistics
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Date Deposited: 21 Jun 2021 13:27
Last Modified: 01 Jul 2021 23:17

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics