# Generalized Linear Bandits with Local Differential Privacy

arXiv: https://arxiv.org/abs/2106.03365 · HTML: https://mlsanity.com/paper/2106.03365/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Mostly Exploration-Free Algorithms for Contextual Bandits](https://mlsanity.com/paper/1704.09011/) (2017)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [A Contextual Bandit Bake-off](https://mlsanity.com/paper/1802.04064/) (2018)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Hedging the Drift: Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1903.01461/) (2019)
- [Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12](https://mlsanity.com/paper/1709.02753/) (2017)
- [Multi-Armed Bandits with Local Differential Privacy](https://mlsanity.com/paper/2007.03121/) (2020)
- [An Efficient Algorithm For Generalized Linear Bandit: Online Stochastic Gradient Descent and Thompson Sampling](https://mlsanity.com/paper/2006.04012/) (2020)
- [Practical Locally Private Heavy Hitters](https://mlsanity.com/paper/1707.04982/) (2017)
- [Differential Privacy for Multi-armed Bandits: What Is It and What Is Its Cost?](https://mlsanity.com/paper/1905.12298/) (2019)
- [Privacy-Preserving Dynamic Personalized Pricing with Demand Learning](https://mlsanity.com/paper/2009.12920/) (2020)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [The Externalities of Exploration and How Data Diversity Helps Exploitation](https://mlsanity.com/paper/1806.00543/) (2018)
- [(Locally) Differentially Private Combinatorial Semi-Bandits](https://mlsanity.com/paper/2006.00706/) (2020)

## Built on by (most cited first, 29 of 29)

- [Shuffle Private Linear Contextual Bandits](https://mlsanity.com/paper/2202.05567/) (2022)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [Differentially Private Stochastic Linear Bandits: (Almost) for Free](https://mlsanity.com/paper/2207.03445/) (2022)
- [Multi-channel Autobidding with Budget and ROI Constraints](https://mlsanity.com/paper/2302.01523/) (2023)
- [Differential Privacy in Personalized Pricing with Nonparametric Demand Models](https://mlsanity.com/paper/2109.04615/) (2021)
- [Federated Linear Contextual Bandits with User-level Differential Privacy](https://mlsanity.com/paper/2306.05275/) (2023)
- [Efficient Algorithms for Generalized Linear Bandits with Heavy-tailed Rewards](https://mlsanity.com/paper/2310.18701/) (2023)
- [Dynamic Global Sensitivity for Differentially Private Contextual Bandits](https://mlsanity.com/paper/2208.14555/) (2022)
- [Differentially Private Kernelized Contextual Bandits](https://mlsanity.com/paper/2501.07046/) (2025)
- [KL-regularization Itself is Differentially Private in Bandits and RLHF](https://mlsanity.com/paper/2505.18407/) (2025)
- [Concurrent Shuffle Differential Privacy Under Continual Observation](https://mlsanity.com/paper/2301.12535/) (2023)
- [On the Optimal Regret of Locally Private Linear Contextual Bandit](https://mlsanity.com/paper/2404.09413/) (2024)
- [On Private Online Convex Optimization: Optimal Algorithms in ℓp-Geometry and High Dimensional Contextual Bandits](https://mlsanity.com/paper/2206.08111/) (2022)
- [Privacy Preserving Adaptive Experiment Design](https://mlsanity.com/paper/2401.08224/) (2024)
- [FLIPHAT: Joint Differential Privacy for High Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2405.14038/) (2024)
- [Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2602.00417/) (2026)
- [Vertical Federated Linear Contextual Bandits](https://mlsanity.com/paper/2210.11050/) (2022)
- [Robust and differentially private stochastic linear bandits](https://mlsanity.com/paper/2304.11741/) (2023)
- [Differentially Private High Dimensional Bandits](https://mlsanity.com/paper/2402.03737/) (2024)
- [Privacy-Preserving Dynamic Assortment Selection](https://mlsanity.com/paper/2410.22488/) (2024)
- [Private Selection with Heterogeneous Sensitivities](https://mlsanity.com/paper/2501.05309/) (2025)
- [Locally Private Nonparametric Contextual Multi-armed Bandits](https://mlsanity.com/paper/2503.08098/) (2025)
- [The Safety-Privacy Tradeoff in Linear Bandits](https://mlsanity.com/paper/2504.16371/) (2025)
- [Optimal Regret of Bernoulli Bandits under Global Differential Privacy](https://mlsanity.com/paper/2505.05613/) (2025)
- [Scalable and Interpretable Contextual Bandits: A Literature Review and Retail Offer Prototype](https://mlsanity.com/paper/2505.16918/) (2025)
- [Differential Privacy in Kernelized Contextual Bandits via Random Projections](https://mlsanity.com/paper/2507.13639/) (2025)
- [Locally Differentially Private Thresholding Bandits](https://mlsanity.com/paper/2507.23073/) (2025)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Online Survival Analysis: A Bandit Approach under Cox PH Model](https://mlsanity.com/paper/2604.20296/) (2026)

## Abstract (arXiv)

Contextual bandit algorithms are useful in personalized online decision-making. However, many applications such as personalized medicine and online advertising require the utilization of individual-specific information for effective learning, while user's data should remain private from the server due to privacy concerns. This motivates the introduction of local differential privacy (LDP), a stringent notion in privacy, to contextual bandits. In this paper, we design LDP algorithms for stochastic generalized linear bandits to achieve the same regret bound as in non-privacy settings. Our main idea is to develop a stochastic gradient-based estimator and update mechanism to ensure LDP. We then exploit the flexibility of stochastic gradient descent (SGD), whose theoretical guarantee for bandit problems is rarely explored, in dealing with generalized linear bandits. We also develop an estimator and update mechanism based on Ordinary Least Square (OLS) for linear bandits. Finally, we conduct experiments with both simulation and real-world datasets to demonstrate the consistently superb performance of our algorithms under LDP constraints with reasonably small parameters (varepsilon, δ) to ensure strong privacy protection.