Differentially Private Regret Minimization in Episodic Markov Decision Processes
This addresses privacy protection in reinforcement learning for real-world sequential decision-making, offering incremental improvements with specific privacy guarantees.
The paper tackles regret minimization in episodic Markov decision processes under differential privacy constraints, proposing frameworks for policy optimization and value iteration that achieve sublinear regret with privacy costs being additive for joint DP and multiplicative for local DP.
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.