No-regret Exploration in Shuffle Private Reinforcement Learning

Abstract: Differential privacy (DP) has recently been introduced into episodic reinforcement learning (RL) to formally address user privacy concerns in personalized services. Previous work mainly focuses on two trust models of DP: the central model, where a central agent is responsible for protecting users' sensitive data, and the (stronger) local model, where the protection occurs directly on the user side. However, they either require a trusted central agent or incur a significantly higher privacy cost, making it unsuitable for many scenarios. This work introduces a trust model stronger than the central model but with a lower privacy cost than the local model, leveraging the emerging \emph{shuffle} model of privacy. We present the first generic algorithm for episodic RL under the shuffle model, where a trusted shuffler randomly permutes a batch of users' data before sending it to the central agent. We then instantiate the algorithm using our proposed shuffle Privatizer, relying on a shuffle private binary summation mechanism. Our analysis shows that the algorithm achieves a near-optimal regret bound comparable to that of the centralized model and significantly outperforms the local model in terms of privacy cost.