Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits
Sahasrajit Sarmasarkar
TL;DR
This work introduces the first algorithms for generalized linear contextual bandits under shuffle differential privacy and joint differential privacy. It tackles three core challenges: private optimization without closed-form estimators, continual noisy updates to design matrices, and privacy-preserving handling of policy switches. The shuffle-DP algorithm achieves $\tilde{O}(d^{3/2}\sqrt{T}/\sqrt{\varepsilon})$ regret under stochastic contexts, while the JDP algorithm achieves $\tilde{O}(d\sqrt{T}/\sqrt{\varepsilon})$ under adversarial contexts, both with leading terms free of the potentially exponential instance parameter $\kappa$ and without spectral assumptions on context distributions. The results bridge a gap between private linear bandits and private GLMs, demonstrating practical DP applicability in GLM-based contextual decision tasks and offering a framework for future tightening of DP-regret tradeoffs. The work combines private convex optimization via shuffle mechanisms, batched and binary-tree release strategies, and novel privacy analyses of policy-switching, contributing to both theory and potential real-world deployments where sensitive contextual data must remain private.
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 $\tilde{O}(d^{3/2}\sqrt{T}/\sqrt{\varepsilon})$ regret. For adversarial contexts, we provide a joint-DP algorithm with $\tilde{O}(d\sqrt{T}/\sqrt{\varepsilon})$ regret -- matching the non-private rate up to a $1/\sqrt{\varepsilon}$ factor. Both algorithms remove dependence on the instance-specific parameter $κ$ (which can be exponential in dimension) from the dominant $\sqrt{T}$ term. Unlike prior work on locally private GLM bandits, our methods require no spectral assumptions on the context distribution beyond $\ell_2$ boundedness.