# The Safety-Privacy Tradeoff in Linear Bandits

arXiv: https://arxiv.org/abs/2504.16371 · HTML: https://mlsanity.com/paper/2504.16371/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 23 Apr 2025.

## Builds on (most cited first, 17 of 17)

- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Differentially-Private Federated Linear Bandits](https://mlsanity.com/paper/2010.11425/) (2020)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [Stochastic Bandits with Linear Constraints](https://mlsanity.com/paper/2006.10185/) (2020)
- [Locally Differentially Private (Contextual) Bandits Learning](https://mlsanity.com/paper/2006.00701/) (2020)
- [Algorithms for Differentially Private Multi-Armed Bandits](https://mlsanity.com/paper/1511.08681/) (2015)
- [Generalized Linear Bandits with Local Differential Privacy](https://mlsanity.com/paper/2106.03365/) (2021)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [Optimal Rates of (Locally) Differentially Private Heavy-tailed Multi-Armed Bandits](https://mlsanity.com/paper/2106.02575/) (2021)
- [Differentially Private Stochastic Linear Bandits: (Almost) for Free](https://mlsanity.com/paper/2207.03445/) (2022)
- [(Locally) Differentially Private Combinatorial Semi-Bandits](https://mlsanity.com/paper/2006.00706/) (2020)
- [Safe Online Convex Optimization with Unknown Linear Safety Constraints](https://mlsanity.com/paper/2111.07430/) (2021)
- [Reviewing and Improving the Gaussian Mechanism for Differential Privacy](https://mlsanity.com/paper/1911.12060/) (2019)
- [Correlational Dueling Bandits with Application to Clinical Treatment in Large Decision Spaces](https://mlsanity.com/paper/1707.02375/) (2017)
- [Rate-Optimal Online Convex Optimization in Adaptive Linear Control](https://mlsanity.com/paper/2206.01426/) (2022)
- [The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedback](https://mlsanity.com/paper/2305.00889/) (2023)
- [Safe Pricing Mechanisms for Distributed Resource Allocation with Bandit Feedback](https://mlsanity.com/paper/2307.15785/) (2023)

## Abstract (arXiv)

We consider a collection of linear stochastic bandit problems, each modeling the random response of different agents to proposed interventions, coupled together by a global safety constraint. We assume a central coordinator must choose actions to play on each bandit with the objective of regret minimization, while also ensuring that the expected response of all agents satisfies the global safety constraints at each round, in spite of uncertainty about the bandits' parameters. The agents consider their observed responses to be private and in order to protect their sensitive information, the data sharing with the central coordinator is performed under local differential privacy (LDP). However, providing higher level of privacy to different agents would have consequences in terms of safety and regret. We formalize these tradeoffs by building on the notion of the sharpness of the safety set - a measure of how the geometric properties of the safe set affects the growth of regret - and propose a unilaterally unimprovable vector of privacy levels for different agents given a maximum regret budget.