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Poster
(Locally) Differentially Private Combinatorial Semi-Bandits
Xiaoyu Chen · Kai Zheng · Zixin Zhou · Yunchang Yang · Wei Chen · Liwei Wang

Wed Jul 15 08:00 AM -- 08:45 AM & Wed Jul 15 09:00 PM -- 09:45 PM (PDT) @
in Poster Session 22 »
In this paper, we study Combinatorial Semi-Bandits (CSB) that is an extension of classic Multi-Armed Bandits (MAB) under Differential Privacy (DP) and stronger Local Differential Privacy (LDP) setting. Since the server receives more information from users in CSB, it usually causes additional dependence on the dimension of data, which is a notorious side-effect for privacy preserving learning. However for CSB under two common smoothness assumptions, we show it is possible to remove this side-effect. In detail, for $B_{\infty}$-bounded smooth CSB under either $\varepsilon$-LDP or $\varepsilon$-DP, we prove the optimal regret bound is $\Theta(\frac{mB^2_{\infty}\ln T } {\Delta\varepsilon^2})$ or $\tilde{\Theta}(\frac{mB^2_{\infty}\ln T} { \Delta\varepsilon})$ respectively, where $T$ is time period, $\Delta$ is the gap of rewards and $m$ is the number of base arms, by proposing novel algorithms and matching lower bounds. For $B_1$-bounded smooth CSB under $\varepsilon$-DP, we also prove the optimal regret bound is $\tilde{\Theta}(\frac{mKB^2_1\ln T} {\Delta\varepsilon})$ with both upper bound and lower bound, where $K$ is the maximum number of feedback in each round. All above results nearly match corresponding non-private optimal rates, which imply there is no additional price for (locally) differentially private CSB in above common settings.
Keywords: Privacy-preserving Statistics and Machine Learning · Online Learning / Bandits

Author Information

Xiaoyu Chen (Peking University)
Kai Zheng (Peking University)
Zixin Zhou (Peking University)
Yunchang Yang (Center for Data Science, Peking University)
Wei Chen (Microsoft)
Liwei Wang (Peking University)

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