Differentially Private Episodic Reinforcement Learning with Heavy-tailed Rewards

Yulian Wu, Xingyu Zhou, Sayak Ray Chowdhury, Di Wang*

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

Abstract

In this paper, we study the problem of (finite horizon tabular) Markov decision processes (MDPs) with heavy-tailed rewards under the constraint of differential privacy (DP). Compared with the previous studies for private reinforcement learning that typically assume rewards are sampled from some bounded or sub-Gaussian distributions to ensure DP, we consider the setting where reward distributions have only finite (1 + v)-th moments with some v ∈ (0, 1]. By resorting to robust mean estimators for rewards, we first propose two frameworks for heavy-tailed MDPs, i.e., one is for value iteration and another is for policy optimization. Under each framework, we consider both joint differential privacy (JDP) and local differential privacy (LDP) models. Based on our frameworks, we provide regret upper bounds for both JDP and LDP cases and show that the moment of distribution and privacy budget both have significant impacts on regrets. Finally, we establish a lower bound of regret minimization for heavy-tailed MDPs in JDP model by reducing it to the instance-independent lower bound of heavy-tailed multi-armed bandits in DP model. We also show the lower bound for the problem in LDP by adopting some private minimax methods. Our results reveal that there are fundamental differences between the problem of private RL with sub-Gaussian and that with heavy-tailed rewards.

Original languageEnglish (US)
Pages37880-37918
Number of pages39
StatePublished - 2023
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: Jul 23 2023Jul 29 2023

Conference

Conference40th International Conference on Machine Learning, ICML 2023
Country/TerritoryUnited States
CityHonolulu
Period07/23/2307/29/23

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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