[2406.06408] Differentially Private Best-Arm Identification

Statistics > Machine Learning arXiv:2406.06408 (stat) [Submitted on 10 Jun 2024 (v1), last revised 8 Apr 2026 (this version, v2)] Title:Differentially Private Best-Arm Identification Authors:Achraf Azize, Marc Jourdan, Aymen Al Marjani, Debabrota Basu View a PDF of the paper titled Differentially Private Best-Arm Identification, by Achraf Azize and 3 other authors View PDF Abstract:Best Arm Identification (BAI) problems are progressively used for data-sensitive applications, such as designing adaptive clinical trials, tuning hyper-parameters, and conducting user studies. Motivated by the data privacy concerns invoked by these applications, we study the problem of BAI with fixed confidence in both the local and central models, i.e. $\epsilon$-local and $\epsilon$-global Differential Privacy (DP). First, to quantify the cost of privacy, we derive lower bounds on the sample complexity of any $\delta$-correct BAI algorithm satisfying $\epsilon$-global DP or $\epsilon$-local DP. Our lower bounds suggest the existence of two privacy regimes. In the high-privacy regime, the hardness depends on a coupled effect of privacy and novel information-theoretic quantities involving the Total Variation. In the low-privacy regime, the lower bounds reduce to the non-private lower bounds. We propose $\epsilon$-local DP and $\epsilon$-global DP variants of a Top Two algorithm, namely CTB-TT and AdaP-TT*, respectively. For $\epsilon$-local DP, CTB-TT is asymptotically optimal by plugging in a p...