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## Algorithms for Differentially Private Multi-Armed Bandits

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Aristide C. Y. Tossou
• Function : Author
Christos Dimitrakakis

#### 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.

### Dates and versions

hal-01234427 , version 1 (26-11-2015)

### Identifiers

• HAL Id : hal-01234427 , version 1
• ARXIV :

### Cite

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

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