Achieving Privacy in the Adversarial Multi-Armed Bandit

In this paper, we improve the previously best known regret bound to achieve ϵ-differential privacy in oblivious adversarial bandits from O(T2/3/ϵ) to O(T−−√lnT/ϵ). This is achieved by combining a Laplace Mechanism with EXP3. We show that though EXP3 is already differentially private, it leaks a linear amount of information in T. However, we can improve this privacy by relying on its intrinsic exponential mechanism for selecting actions. This allows us to reach O(lnT−−−√)-DP, with a regret of O(T2/3) that holds against an adaptive adversary, an improvement from the best known of O(T3/4). This is done by using an algorithm that run EXP3 in a mini-batch loop. Finally, we run experiments that clearly demonstrate the validity of our theoretical analysis.