  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, PRL, 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 $\frac{\ln(1/\delta)^{1/4}}{\epsilon^{1/2}}$
given privacy parameters $\epsilon, \delta > 0$. 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.
