Locally Differentially Private Thresholding Bandits

Annalisa Barbara, Joseph Lazzaro, Ciara Pike-Burke

Keywords: multi-armed bandits, pure exploration, differential privacy

TL;DR: We study thresholding bandits under local differential privacy and propose near-optimal algorithms in both fixed budget and fixed confidence settings.

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.

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Serve As Reviewer: ~Joseph_Lazzaro1

Track: Regular Track: unpublished work

Submission Number: 147