Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits

TL;DR

This paper introduces the first algorithms for generalized linear contextual bandits that ensure shuffle and joint differential privacy, addressing key challenges with new privacy-preserving optimization techniques.

Contribution

It develops novel private algorithms for GLM bandits under shuffle and joint differential privacy, overcoming the lack of closed-form estimators and tracking privacy across evolving data.

Findings

Shuffle-DP algorithm achieves regret close to non-private in stochastic contexts.

Joint-DP algorithm matches non-private regret in adversarial contexts with an additive privacy cost.

No spectral assumptions needed beyond boundedness for context distributions.

Abstract

We present the first algorithms for generalized linear contextual bandits under shuffle differential privacy and joint differential privacy. While prior work on private contextual bandits has been restricted to linear reward models -- which admit closed-form estimators -- generalized linear models (GLMs) pose fundamental new challenges: no closed-form estimator exists, requiring private convex optimization; privacy must be tracked across multiple evolving design matrices; and optimization error must be explicitly incorporated into regret analysis. We address these challenges under two privacy models and context settings. For stochastic contexts, we design a shuffle-DP algorithm achieving $\tilde{O}(d^{3/2}\sqrt{T \log T}/\sqrt{\varepsilon})$ regret in dominant term, differing from the non-private rate by a factor of $\sqrt{d/\varepsilon}$. For adversarial contexts, we provide a joint-DP algorithm with regret $\tilde{O}\!\big(d\sqrt{T} \log T + d^{3/4}\sqrt{T/\varepsilon}\,(\log T)\,(d + \log T)^{1/4}\big)$ -- matching the non-private rate $\tilde{O}(d\sqrt{T} \log T)$ in the leading term, with privacy contributing only an additive correction. Unlike prior work on locally private GLM bandits, our methods require no spectral assumptions on the context distribution beyond $\ell_2$ boundedness.