Locally Differentially Private Thresholding Bandits
This work addresses privacy-preserving decision-making in bandit problems, which is incremental as it applies known privacy techniques to a specific bandit setting.
The paper tackles the thresholding bandit problem under local differential privacy constraints, proposing algorithms that use a Bernoulli-based private mechanism to identify arms above a threshold, with theoretical bounds showing they match lower bounds up to poly-logarithmic factors.
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.