Adaptive Control of Differentially Private Linear Quadratic Systems

In this paper we study the problem of regret minimization in reinforcement learning (RL) under differential privacy constraints. This work is motivated by the wide range of RL applications for providing personalized service, where privacy concerns are becoming paramount. In contrast to previous works, we take the first step towards non-tabular RL settings, while providing a rigorous privacy guarantee. In particular, we consider the adaptive control of differentially private linear quadratic (LQ) systems. We develop the first private RL algorithm, Private-OFU-RL which is able to attain a sub-linear regret while guaranteeing privacy protection. More importantly, the additional cost due to privacy is only on the order of $\frac{\ln(1/\delta)^{1/4}}{\varepsilon^{1/2}}$ given privacy parameters $\varepsilon, \delta > 0$ . Through this process, we also provide a general procedure for adaptive control of LQ systems under changing regularizers, which not only generalizes previous non-private controls, but also serves as the basis for general private controls.