# Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits

arXiv: https://arxiv.org/abs/2602.00417 · HTML: https://mlsanity.com/paper/2602.00417/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 53 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 30 of 34)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [What Doubling Tricks Can and Can't Do for Multi-Armed Bandits](https://mlsanity.com/paper/1803.06971/) (2018)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2010.12642/) (2020)
- [Locally Differentially Private (Contextual) Bandits Learning](https://mlsanity.com/paper/2006.00701/) (2020)
- [Linear Bandits with Limited Adaptivity and Learning Distributional Optimal Design](https://mlsanity.com/paper/2007.01980/) (2020)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Private Summation in the Multi-Message Shuffle Model](https://mlsanity.com/paper/2002.00817/) (2020)
- [Private Federated Learning Without a Trusted Server: Optimal Algorithms for Convex Losses](https://mlsanity.com/paper/2106.09779/) (2021)
- [Generalized Linear Bandits with Local Differential Privacy](https://mlsanity.com/paper/2106.03365/) (2021)
- [Max-Information, Differential Privacy, and Post-Selection Hypothesis Testing](https://mlsanity.com/paper/1604.03924/) (2016)
- [Shuffle Private Linear Contextual Bandits](https://mlsanity.com/paper/2202.05567/) (2022)
- [Differentially Private Multi-Armed Bandits in the Shuffle Model](https://mlsanity.com/paper/2106.02900/) (2021)
- [Fully Adaptive Composition in Differential Privacy](https://mlsanity.com/paper/2203.05481/) (2022)
- [Generalized Linear Bandits with Limited Adaptivity](https://mlsanity.com/paper/2404.06831/) (2024)
- [Differentially Private Stochastic Linear Bandits: (Almost) for Free](https://mlsanity.com/paper/2207.03445/) (2022)
- [Contexts can be Cheap: Solving Stochastic Contextual Bandits with Linear Bandit Algorithms](https://mlsanity.com/paper/2211.05632/) (2022)
- [A Contextual-bandit-based Approach for Informed Decision-making in Clinical Trials](https://mlsanity.com/paper/1809.00258/) (2018)
- [Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message](https://mlsanity.com/paper/2109.13158/) (2021)
- [Shuffle Private Stochastic Convex Optimization](https://mlsanity.com/paper/2106.09805/) (2021)
- [Privacy Amplification via Shuffling for Linear Contextual Bandits](https://mlsanity.com/paper/2112.06008/) (2021)

## Built on by (most cited first, 1 of 1)

- [Vanilla Policy Optimization Is Both Optimal and Differentially Private for Stochastic Contextual Bandits](https://mlsanity.com/paper/2609.33888/) (2026)

## Abstract (arXiv)

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 tildeO(d3/2√T log T/√varepsilon) regret in dominant term, differing from the non-private rate by a factor of √d/varepsilon. For adversarial contexts, we provide a joint-DP algorithm with regret tildeO!big(d√T log T + d3/4√T/varepsilon,(log T),(d + log T)1/4big) -- matching the non-private rate tildeO(d√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 ℓ2 boundedness.