Cascading Bandit under Differential Privacy

TL;DR

This paper introduces new differentially private algorithms for cascading bandits, achieving improved regret bounds under both central and local privacy models, with extensive experiments validating the theoretical results.

Contribution

The paper proposes novel differentially private algorithms for cascading bandits with improved regret bounds and extends the results to combinatorial semi-bandits.

Findings

Achieves regret of (rac{\u2113 T}{})^{1+} under DP, improving previous bounds.

Provides regret bounds of (rac{K\u2206    T}) under LDP, balancing privacy and error probability.

Validates theoretical results with extensive experiments.

Abstract

This paper studies \emph{differential privacy (DP)} and \emph{local differential privacy (LDP)} in cascading bandits. Under DP, we propose an algorithm which guarantees $\epsilon$-indistinguishability and a regret of $\mathcal{O}((\frac{\log T}{\epsilon})^{1+\xi})$ for an arbitrarily small $\xi$. This is a significant improvement from the previous work of $\mathcal{O}(\frac{\log^3 T}{\epsilon})$ regret. Under ($\epsilon$,$\delta$)-LDP, we relax the $K^2$ dependence through the tradeoff between privacy budget $\epsilon$ and error probability $\delta$, and obtain a regret of $\mathcal{O}(\frac{K\log (1/\delta) \log T}{\epsilon^2})$, where $K$ is the size of the arm subset. This result holds for both Gaussian mechanism and Laplace mechanism by analyses on the composition. Our results extend to combinatorial semi-bandit. We show respective lower bounds for DP and LDP cascading bandits. Extensive experiments corroborate our theoretic findings.