# Concentrated Differential Privacy for Bandits

Source: [Concentrated Differential Privacy for Bandits](<https://www.sota2.com/research/paper/68fa5baa1e209131ce9ca6b3>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:12:40.380Z

Authors: Achraf Azize, Debabrota Basu

Published: 2023-09-01T16:08:00.000Z

## Abstract

Bandits serve as the theoretical foundation of sequential learning and an algorithmic foundation of modern recommender systems. However, recommender systems often rely on user-sensitive data, making privacy a critical concern. This paper contributes to the understanding of Differential Privacy (DP) in bandits with a trusted centralised decision-maker, and especially the implications of ensuring zero Concentrated Differential Privacy (zCDP). First, we formalise and compare different adaptations of DP to bandits, depending on the considered input and the interaction protocol. Then, we propose three private algorithms, namely AdaC-UCB, AdaC-GOPE and AdaC-OFUL, for three bandit settings, namely finite-armed bandits, linear bandits, and linear contextual bandits. The three algorithms share a generic algorithmic blueprint, i.e. the Gaussian mechanism and adaptive episodes, to ensure a good privacy-utility trade-off. We analyse and upper bound the regret of these three algorithms. Our analysis shows that in all of these settings, the prices of imposing zCDP are (asymptotically) negligible in comparison with the regrets incurred oblivious to privacy. Next, we complement our regret upper bounds with the first minimax lower bounds on the regret of bandits with zCDP. To prove the lower bounds, we elaborate a new proof technique based on couplings and optimal transport. We conclude by experimentally validating our theoretical results for the three different settings of bandits.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Contextual Bandits on MovieLens 25M](<https://www.sota2.com/research/sota/contextual-bandits-on-movielens-25m.md>): Contextual Bandits; MovieLens 25M; Success Rate vs Non-Private LinUCB: 84.7.

- [Contextual Bandits on Jester](<https://www.sota2.com/research/sota/contextual-bandits-on-jester.md>): Contextual Bandits; Jester; Non-private LinUCB Performance: 76.3.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2309.00557>)

[PDF](<https://arxiv.org/pdf/2309.00557.pdf>)