Differentially Private Regret Minimization in Episodic Markov Decision Processes

Abstract

We study regret minimization in finite horizon tabular Markov decision processes (MDPs) under the constraints of differential privacy (DP). This is motivated by the widespread applications of reinforcement learning (RL) in real-world sequential decision making problems, where protecting users' sensitive and private information is becoming paramount. We consider two variants of DP -- joint DP (JDP), where a centralized agent is responsible for protecting users' sensitive data and local DP (LDP), where information needs to be protected directly on the user side. We first propose two general frameworks -- one for policy optimization and another for value iteration -- for designing private, optimistic RL algorithms. We then instantiate these frameworks with suitable privacy mechanisms to satisfy JDP and LDP requirements, and simultaneously obtain sublinear regret guarantees. The regret bounds show that under JDP, the cost of privacy is only a lower order additive term, while for a stronger privacy protection under LDP, the cost suffered is multiplicative. Finally, the regret bounds are obtained by a unified analysis, which, we believe, can be extended beyond tabular MDPs.

Concurrent Shuffle Differential Privacy Under Continual Observation

“…Other works considered ℓ p extensions, high dimensional variants, or improvements and applications of PSCO. 4 Several works have studied the private multiarmed bandit problem (Mishra & Thakurta, 2015;Tossou & Dimitrakakis, 2017;Sajed & Sheffet, 2019;Ren et al, 2020a;Chen et al, 2020;Zhou & Tan, 2021;Dubey, 2021), the private contextual linear bandit problem (Shariff & Sheffet, 2018;Zheng et al, 2020;Han et al, 2020;Ren et al, 2020b;Garcelon et al, 2022), and the more general private reinforcement learning (Vietri et al, 2020;Garcelon et al, 2021;Chowdhury & Zhou, 2022a) problem, in both local and centralized models of privacy. The regret gap between the two models (when the contexts are arbitrary, not stochastic (Han et al, 2021)) has shrunk using the intermediate sequential shuffle model (Tenenbaum et al, 2021;Chowdhury & Zhou, 2022b;Garcelon et al, 2022).…”