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  • Publication
    Accès libre
    Differential Privacy for Multi-armed Bandits: What Is It and What Is Its Cost?
    (2019)
    Debabrota Basu
    ;
    ;
    Aristide Tossou
    Based on differential privacy (DP) framework, we introduce and unify privacy definitions for the multi-armed bandit algorithms. We represent the framework with a unified graphical model and use it to connect privacy definitions. We derive and contrast lower bounds on the regret of bandit algorithms satisfying these definitions. We leverage a unified proving technique to achieve all the lower bounds. We show that for all of them, the learner's regret is increased by a multiplicative factor dependent on the privacy level ϵ. We observe that the dependency is weaker when we do not require local differential privacy for the rewards.
  • Publication
    Accès libre
    Algorithms for Differentially Private Multi-Armed Bandits
    (2016)
    Aristide Tossou
    ;
    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 (ϵ,δ) differentially private variants of Upper Confidence Bound algorithms which have optimal regret, O(ϵ−1+logT). This is a significant improvement over previous results, which only achieve poly-log regret O(ϵ−2log2T), 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.