Dynamic Global Sensitivity for Differentially Private Contextual Bandits

TL;DR

This paper introduces a differentially private linear contextual bandit algorithm that adaptively reduces noise over time using dynamic global sensitivity, balancing privacy and regret in recommendation systems.

Contribution

It presents a novel dynamic global sensitivity approach for privacy-preserving bandits, enabling less noise injection and improved regret bounds compared to existing methods.

Findings

The algorithm achieves $(psilon, elta)$-differential privacy with lower regret.

Theoretical analysis confirms the shrinking sensitivity and regret bounds.

Experimental results demonstrate superiority over existing solutions.

Abstract

Bandit algorithms have become a reference solution for interactive recommendation. However, as such algorithms directly interact with users for improved recommendations, serious privacy concerns have been raised regarding its practical use. In this work, we propose a differentially private linear contextual bandit algorithm, via a tree-based mechanism to add Laplace or Gaussian noise to model parameters. Our key insight is that as the model converges during online update, the global sensitivity of its parameters shrinks over time (thus named dynamic global sensitivity). Compared with existing solutions, our dynamic global sensitivity analysis allows us to inject less noise to obtain $(\epsilon, \delta)$-differential privacy with added regret caused by noise injection in $\tilde O(\log{T}\sqrt{T}/\epsilon)$. We provide a rigorous theoretical analysis over the amount of noise added via dynamic global sensitivity and the corresponding upper regret bound of our proposed algorithm. Experimental results on both synthetic and real-world datasets confirmed the algorithm's advantage against existing solutions.