Locally Differentially Private Thresholding Bandits

TL;DR

This paper develops differentially private algorithms for thresholding bandit problems, balancing privacy guarantees with performance, and establishes theoretical bounds showing near-optimality of the proposed methods.

Contribution

It introduces private response mechanisms for thresholding bandits and derives tight bounds, advancing privacy-preserving bandit algorithms.

Findings

Algorithms achieve strong privacy guarantees.

Performance bounds match lower bounds up to poly-log factors.

Provides insights into privacy-utility trade-offs in bandit problems.

Abstract

This work investigates the impact of ensuring local differential privacy in the thresholding bandit problem. We consider both the fixed budget and fixed confidence settings. We propose methods that utilize private responses, obtained through a Bernoulli-based differentially private mechanism, to identify arms with expected rewards exceeding a predefined threshold. We show that this procedure provides strong privacy guarantees and derive theoretical performance bounds on the proposed algorithms. Additionally, we present general lower bounds that characterize the additional loss incurred by any differentially private mechanism, and show that the presented algorithms match these lower bounds up to poly-logarithmic factors. Our results provide valuable insights into privacy-preserving decision-making frameworks in bandit problems.