The Price of Differential Privacy For Online Learning

Abstract

We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal $\tilde{O}(\sqrt{T})$ regret bounds. In the full-information setting, our results demonstrate that $ε$-differential privacy may be ensured for free -- in particular, the regret bounds scale as $O(\sqrt{T})+\tilde{O}\left(\frac{1}ε\right)$. For bandit linear optimization, and as a special case, for non-stochastic multi-armed bandits, the proposed algorithm achieves a regret of $\tilde{O}\left(\frac{1}ε\sqrt{T}\right)$, while the previously known best regret bound was $\tilde{O}\left(\frac{1}εT^{\frac{2}{3}}\right)$.

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