Biblio

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 \$\textbackslashtextbackslashfrac\textbackslashtextbackslashln(1/\textbackslashtextbackslashdelta)ˆ1/4\textbackslashtextbackslashvarepsilonˆ1/2\$ given privacy parameters \$\textbackslashtextbackslashvarepsilon, \textbackslashtextbackslashdelta \textbackslashtextgreater 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.

There has been significant interest in studying security games for modeling the interplay of attacks and defenses on various systems involving critical infrastructure, financial system security, political campaigns, and civil safeguarding. However, existing security game models typically either assume additive utility functions, or that the attacker can attack only one target. Such assumptions lead to tractable analysis, but miss key inherent dependencies that exist among different targets in current complex networks. In this paper, we generalize the classical security game models to allow for non-additive utility functions. We also allow attackers to be able to attack multiple targets. We examine such a general security game from a theoretical perspective and provide a unified view. In particular, we show that each security game is equivalent to a combinatorial optimization problem over a set system ε, which consists of defender's pure strategy space. The key technique we use is based on the transformation, projection of a polytope, and the ellipsoid method. This work settles several open questions in security game domain and extends the state-of-the-art of both the polynomial solvable and NP-hard class of the security game.