Privacy Amplification via Shuffling for Linear Contextual Bandits

TL;DR

This paper introduces a privacy-preserving algorithm for linear contextual bandits using the shuffle model, achieving a balance between joint and local differential privacy with a favorable regret bound.

Contribution

It demonstrates that the shuffle model can be used to attain a privacy-utility trade-off in contextual bandits, bridging the gap between joint and local differential privacy.

Findings

Achieves regret bound of O(T^{2/3}/^{1/3}) with privacy guarantees.

Leverages shuffling and batching to balance privacy and utility.

Provides theoretical analysis of privacy-utility trade-off in bandit algorithms.

Abstract

Contextual bandit algorithms are widely used in domains where it is desirable to provide a personalized service by leveraging contextual information, that may contain sensitive information that needs to be protected. Inspired by this scenario, we study the contextual linear bandit problem with differential privacy (DP) constraints. While the literature has focused on either centralized (joint DP) or local (local DP) privacy, we consider the shuffle model of privacy and we show that is possible to achieve a privacy/utility trade-off between JDP and LDP. By leveraging shuffling from privacy and batching from bandits, we present an algorithm with regret bound $\widetilde{\mathcal{O}}(T^{2/3}/\varepsilon^{1/3})$, while guaranteeing both central (joint) and local privacy. Our result shows that it is possible to obtain a trade-off between JDP and LDP by leveraging the shuffle model while preserving local privacy.