An Optimal Private Stochastic-MAB Algorithm based on Optimal Private Stopping Rule

Abstract

We present a provably optimal differentially private algorithm for the stochastic multi-arm bandit problem, as opposed to the private analogue of the UCB-algorithm (Mishra and Thakurta, 2015; Tossou and Dimitrakakis, 2016) which doesn’t meet the recently discovered lower-bound of $\Omega \left(\frac{K\log(T)}{\epsilon} \right)$ (Shariff and Sheffet, 2018). Our construction is based on a different algorithm, Successive Elimination (Even-Dar et al., 2002), that repeatedly pulls all remaining arms until an arm is found to be suboptimal and is then eliminated. In order to devise a private analogue of Successive Elimination we visit the problem of private