Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits

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 with regret $\tilde{O}\!\big(d^{3/2}\sqrt{T \log T} + d^{5/4} \sqrt{T/\varepsilon} (\log T)^{3/4}\big)$ in the dominant term, matching the non-private rate $\tilde{O}(d \sqrt{T \log T})$ in the leading-in-$T$ term up to a multiplicative factor of $\sqrt d$ and a privacy correction term of $\tilde{O}(d^{5/4}\sqrt{T \log T/\varepsilon})$. 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. Unlike prior work on locally private GLM bandits, our methods require no spectral assumptions on the context distribution beyond $\ell_2$ boundedness.