Differentially Private Exploration in Reinforcement Learning with Linear Representation

Abstract: This paper studies privacy-preserving exploration in Markov Decision Processes (MDPs) with linear representation. We first consider the setting of linear-mixture MDPs (Ayoub et al., 2020) (a.k.a.\ model-based setting) and provide an unified framework for analyzing joint and local differential private (DP) exploration. Through this framework, we prove a $\widetilde{O}(K<sup>{3/4}/\sqrt{\epsilon})$ regret bound for $(\epsilon,\delta)$-local DP exploration and a $\widetilde{O}(\sqrt{K/\epsilon})$ regret bound for $(\epsilon,\delta)$-joint DP. We further study privacy-preserving exploration in linear MDPs (Jin et al., 2020) (a.k.a.\ model-free setting) where we provide a $$\widetilde{O}\left(K<sup>{\frac{3}{5}}/\epsilon<sup>{\frac{2}{5}}\right)$$ regret bound for $(\epsilon,\delta)$-joint DP, with a novel algorithm based on low-switching. Finally, we provide insights into the issues of designing local DP algorithms in this model-free setting.