Differentially Private Stochastic Linear Bandits: (Almost) for Free

TL;DR

This paper introduces differentially private algorithms for stochastic linear bandits across various models, achieving near-optimal regret bounds and demonstrating that privacy can be maintained with minimal impact on performance.

Contribution

The authors develop differentially private algorithms for linear bandits in central, local, and shuffled models, achieving regret bounds close to non-private algorithms, thus nearly providing privacy for free.

Findings

Achieve regret of  ((T}+rac{1}{\u03B5}) in the central model.

Match non-private regret for constant B5 in the local model, with penalties for small B5.

Attain regret of (T+rac{1}{B5}) in the shuffled model, outperforming previous algorithms.

Abstract

In this paper, we propose differentially private algorithms for the problem of stochastic linear bandits in the central, local and shuffled models. In the central model, we achieve almost the same regret as the optimal non-private algorithms, which means we get privacy for free. In particular, we achieve a regret of $\tilde{O}(\sqrt{T}+\frac{1}{\epsilon})$ matching the known lower bound for private linear bandits, while the best previously known algorithm achieves $\tilde{O}(\frac{1}{\epsilon}\sqrt{T})$. In the local case, we achieve a regret of $\tilde{O}(\frac{1}{\epsilon}{\sqrt{T}})$ which matches the non-private regret for constant $\epsilon$, but suffers a regret penalty when $\epsilon$ is small. In the shuffled model, we also achieve regret of $\tilde{O}(\sqrt{T}+\frac{1}{\epsilon})$ %for small $\epsilon$ as in the central case, while the best previously known algorithm suffers a regret of $\tilde{O}(\frac{1}{\epsilon}{T^{3/5}})$. Our numerical evaluation validates our theoretical results.