# On Differentially Private Federated Linear Contextual Bandits

arXiv: https://arxiv.org/abs/2302.13945 · HTML: https://mlsanity.com/paper/2302.13945/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 43 references that are in the map.
- First posted on arXiv 27 Feb 2023.

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

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Introducing LETOR 4.0 Datasets](https://mlsanity.com/paper/1306.2597/) (2013)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Differentially-Private Federated Linear Bandits](https://mlsanity.com/paper/2010.11425/) (2020)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [The Privacy Blanket of the Shuffle Model](https://mlsanity.com/paper/1903.02837/) (2019)
- [Federated Linear Contextual Bandits](https://mlsanity.com/paper/2110.14177/) (2021)
- [Locally Differentially Private (Contextual) Bandits Learning](https://mlsanity.com/paper/2006.00701/) (2020)
- [Composition of Differential Privacy & Privacy Amplification by Subsampling](https://mlsanity.com/paper/2210.00597/) (2022)
- [An Optimal Private Stochastic-MAB Algorithm Based on an Optimal Private Stopping Rule](https://mlsanity.com/paper/1905.09383/) (2019)
- [Multi-Armed Bandits with Local Differential Privacy](https://mlsanity.com/paper/2007.03121/) (2020)
- [On Privacy and Personalization in Cross-Silo Federated Learning](https://mlsanity.com/paper/2206.07902/) (2022)
- [Private Federated Learning Without a Trusted Server: Optimal Algorithms for Convex Losses](https://mlsanity.com/paper/2106.09779/) (2021)
- [A Simple and Provably Efficient Algorithm for Asynchronous Federated Contextual Linear Bandits](https://mlsanity.com/paper/2207.03106/) (2022)
- [When Privacy Meets Partial Information: A Refined Analysis of Differentially Private Bandits](https://mlsanity.com/paper/2209.02570/) (2022)
- [Shuffle Private Linear Contextual Bandits](https://mlsanity.com/paper/2202.05567/) (2022)
- [Private Non-Convex Federated Learning Without a Trusted Server](https://mlsanity.com/paper/2203.06735/) (2022)
- [Differentially Private Multi-Armed Bandits in the Shuffle Model](https://mlsanity.com/paper/2106.02900/) (2021)
- [Differentially Private Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2201.07052/) (2022)
- [Old Dog Learns New Tricks: Randomized UCB for Bandit Problems](https://mlsanity.com/paper/1910.04928/) (2019)
- [Local Differential Privacy for Bayesian Optimization](https://mlsanity.com/paper/2010.06709/) (2020)
- [Differentially Private Stochastic Linear Bandits: (Almost) for Free](https://mlsanity.com/paper/2207.03445/) (2022)
- [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)
- [Distributed Differential Privacy in Multi-Armed Bandits](https://mlsanity.com/paper/2206.05772/) (2022)
- [No-Regret Algorithms for Private Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2102.12467/) (2021)
- [Differentially Private Linear Bandits with Partial Distributed Feedback](https://mlsanity.com/paper/2207.05827/) (2022)

## Built on by (most cited first, 14 of 14)

- [Federated Linear Contextual Bandits with User-level Differential Privacy](https://mlsanity.com/paper/2306.05275/) (2023)
- [Private Heterogeneous Federated Learning Without a Trusted Server Revisited: Error-Optimal and Communication-Efficient Algorithms for Convex Losses](https://mlsanity.com/paper/2407.09690/) (2024)
- [Pure Exploration in Asynchronous Federated Bandits](https://mlsanity.com/paper/2310.11015/) (2023)
- [FedConPE: Efficient Federated Conversational Bandits with Heterogeneous Clients](https://mlsanity.com/paper/2405.02881/) (2024)
- [Improved Bounds for Private and Robust Alignment](https://mlsanity.com/paper/2512.23816/) (2025)
- [Differentially Private Kernelized Contextual Bandits](https://mlsanity.com/paper/2501.07046/) (2025)
- [Learning from End User Data with Shuffled Differential Privacy over Kernel Densities](https://mlsanity.com/paper/2502.14087/) (2025)
- [On the Sample Complexity of Differentially Private Policy Optimization](https://mlsanity.com/paper/2510.21060/) (2025)
- [Fixed-Budget Differentially Private Best Arm Identification](https://mlsanity.com/paper/2401.09073/) (2024)
- [Harnessing the Power of Federated Learning in Federated Contextual Bandits](https://mlsanity.com/paper/2312.16341/) (2023)
- [Federated Online Prediction from Experts with Differential Privacy: Separations and Regret Speed-ups](https://mlsanity.com/paper/2409.19092/) (2024)
- [Batched Stochastic Linear Bandits with 1-Bit Communication Constraints](https://mlsanity.com/paper/2605.30976/) (2026)
- [Federated Linear Bandit Learning via Over-the-Air Computation](https://mlsanity.com/paper/2308.13298/) (2023)
- [When Determinants Are Not Enough: Private Rare Switching](https://mlsanity.com/paper/2605.23131/) (2026)

## Abstract (arXiv)

We consider cross-silo federated linear contextual bandit (LCB) problem under differential privacy, where multiple silos (agents) interact with the local users and communicate via a central server to realize collaboration while without sacrificing each user's privacy. We identify three issues in the state-of-the-art: (i) failure of claimed privacy protection and (ii) incorrect regret bound due to noise miscalculation and (iii) ungrounded communication cost. To resolve these issues, we take a two-step principled approach. First, we design an algorithmic framework consisting of a generic federated LCB algorithm and flexible privacy protocols. Then, leveraging the proposed framework, we study federated LCBs under two different privacy constraints. We first establish privacy and regret guarantees under silo-level local differential privacy, which fix the issues present in state-of-the-art algorithm. To further improve the regret performance, we next consider shuffle model of differential privacy, under which we show that our algorithm can achieve nearly ``optimal'' regret without a trusted server. We accomplish this via two different schemes -- one relies on a new result on privacy amplification via shuffling for DP mechanisms and another one leverages the integration of a shuffle protocol for vector sum into the tree-based mechanism, both of which might be of independent interest. Finally, we support our theoretical results with numerical evaluations over contextual bandit instances generated from both synthetic and real-life data.