Differentially Private Multi-Armed Bandits in the Shuffle ModelDownload PDF

21 May 2021, 20:45 (modified: 24 Oct 2021, 17:26)NeurIPS 2021 PosterReaders: Everyone
Keywords: multi-armed bandits, differential privacy, shuffle model
Abstract: We give an $(\varepsilon,\delta)$-differentially private algorithm for the Multi-Armed Bandit (MAB) problem in the shuffle model with a distribution-dependent regret of $O\left(\left(\sum_{a:\Delta_a>0}\frac{\log T}{\Delta_a}\right)+\frac{k\sqrt{\log\frac{1}{\delta}}\log T}{\varepsilon}\right)$, and a distribution-independent regret of $O\left(\sqrt{kT\log T}+\frac{k\sqrt{\log\frac{1}{\delta}}\log T}{\varepsilon}\right)$, where $T$ is the number of rounds, $\Delta_a$ is the suboptimality gap of the action $a$, and $k$ is the total number of actions. Our upper bound almost matches the regret of the best known algorithms for the centralized model, and significantly outperforms the best known algorithm in the local model.
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