Achieving Privacy in the Adversarial Multi-Armed Bandit
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In this paper, we improve the previously best known regret bound to achieve ϵ-differential privacy in oblivious adversarial bandits from O(T^2/3/ϵ) to O(√(T) T /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(√( T))-DP, with a regret of O(T^2/3) that holds against an adaptive adversary, an improvement from the best known of O(T^3/4). 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.
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