Adaptive Control of Differentially Private Linear Quadratic Systems

TL;DR

This paper introduces PRL, a differentially private reinforcement learning algorithm for linear quadratic systems that achieves sub-linear regret with minimal privacy-related cost, advancing privacy-preserving adaptive control.

Contribution

It presents the first private RL algorithm for non-tabular LQ systems with rigorous privacy guarantees and minimal additional cost, expanding adaptive control under privacy constraints.

Findings

PRL attains sub-linear regret under differential privacy.

Privacy cost is proportional to rac{ ext{ln}(1/ ext{delta})^{1/4}}{ ext{epsilon}^{1/2}}.

Provides a general adaptive control procedure for LQ systems under changing regularizers.

Abstract

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.