Achieving Privacy in the Adversarial Multi-Armed Bandit

In this paper, we improve the previously best known regret bound to achieve -differential privacy in oblivious adversarial bandits from O(T / ) to O( √ T lnT/ ). 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(T ) that holds against an adaptive adversary, an improvement from the best known of O(T ). 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.