Algorithms for Differentially Private Multi-Armed Bandits

Aristide Tossou 1 Christos Dimitrakakis 2, 1, 3
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : We present differentially private algorithms for the stochastic Multi-Armed Bandit (MAB) problem. This is a problem for applications such as adaptive clinical trials, experiment design, and user-targeted advertising where private information is connected to individual rewards. Our major contribution is to show that there exist $(\epsilon, \delta)$ differentially private variants of Upper Confidence Bound algorithms which have optimal regret, $O(\epsilon^{-1} + \log T)$. This is a significant improvement over previous results, which only achieve poly-log regret $O(\epsilon^{-2} \log^{2} T)$, because of our use of a novel interval-based mechanism. We also substantially improve the bounds of previous family of algorithms which use a continual release mechanism. Experiments clearly validate our theoretical bounds.
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Submitted on : Thursday, November 26, 2015 - 9:52:39 PM
Last modification on : Friday, March 22, 2019 - 1:34:53 AM
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  • HAL Id : hal-01234427, version 1
  • ARXIV : 1511.08681

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Aristide Tossou, Christos Dimitrakakis. Algorithms for Differentially Private Multi-Armed Bandits. AAAI 2016, Feb 2016, Phoenix, Arizona, United States. ⟨hal-01234427⟩

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