Locally Differentially Private Thresholding Bandits

2025-07-30

AI Summary

This paper studies the thresholded multi-armed bandit problem under local differential privacy (LDP): identifying arms whose expected reward exceeds a given threshold, subject to fixed budget and confidence constraints. We propose a privacy mechanism based on Bernoulli randomized response and develop a unified algorithmic framework that integrates concentration inequality analysis with information-theoretic lower bound derivation to jointly optimize privacy preservation and decision efficiency. We prove that the proposed algorithm achieves a sample complexity within at most a logarithmic factor of the fundamental information-theoretic lower bound for LDP threshold identification—establishing, for the first time, near-optimal trade-offs among estimation error, privacy loss, and sampling efficiency. Extensive experiments demonstrate its high efficiency and robustness in arm identification under strong LDP guarantees, revealing the intrinsic precision limits of sequential decision-making under privacy constraints.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Impact of local differential privacy on thresholding bandits
• Methods to identify arms exceeding reward threshold privately
• Theoretical bounds on privacy-preserving bandit algorithms

Innovation

• Bernoulli-based differentially private mechanism
• Private responses for threshold identification
• Matching lower bounds up to poly-logarithmic factors