Achieving Privacy in the Adversarial Multi-Armed Bandit
This work addresses privacy concerns in online learning for applications like recommendation systems, but it is incremental as it builds on existing methods like EXP3.
The paper tackles the problem of achieving differential privacy in adversarial multi-armed bandits, improving the regret bound from O(T^{2/3}/ε) to O(√T ln T/ε) and demonstrating an O(√ln T)-DP method with O(T^{2/3}) regret against an adaptive adversary.
In this paper, we improve the previously best known regret bound to achieve $ε$-differential privacy in oblivious adversarial bandits from $\mathcal{O}{(T^{2/3}/ε)}$ to $\mathcal{O}{(\sqrt{T} \ln T /ε)}$. 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 $\mathcal{O}{(\sqrt{\ln T})}$-DP, with a regret of $\mathcal{O}{(T^{2/3})}$ that holds against an adaptive adversary, an improvement from the best known of $\mathcal{O}{(T^{3/4})}$. 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.