Online Bootstrap Inference For Policy Evaluation In Reinforcement Learning

Pratik Ramprasad, Yuantong Li, Zhuoran Yang, Zhaoran Wang, Will Wei Sun*, Guang Cheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The recent emergence of reinforcement learning (RL) has created a demand for robust statistical inference methods for the parameter estimates computed using these algorithms. Existing methods for inference in online learning are restricted to settings involving independently sampled observations, while inference methods in RL have so far been limited to the batch setting. The bootstrap is a flexible and efficient approach for statistical inference in online learning algorithms, but its efficacy in settings involving Markov noise, such as RL, has yet to be explored. In this article, we study the use of the online bootstrap method for inference in RL policy evaluation. In particular, we focus on the temporal difference (TD) learning and Gradient TD (GTD) learning algorithms, which are themselves special instances of linear stochastic approximation under Markov noise. The method is shown to be distributionally consistent for statistical inference in policy evaluation, and numerical experiments are included to demonstrate the effectiveness of this algorithm across a range of real RL environments. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)2901-2914
Number of pages14
JournalJournal of the American Statistical Association
Issue number544
StatePublished - 2023


  • Asymptotic normality
  • Multiplier bootstrap
  • Reinforcement learning
  • Statistical inference
  • Stochastic approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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