# Differentially Private Contextual Linear Bandits

Source: [Differentially Private Contextual Linear Bandits](<https://www.sota2.com/research/paper/68fa64e31e209131cea0721b>)

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

Data updated: 2025-10-25T21:13:58.604Z

Authors: Roshan Shariff, Or Sheffet

Published: 2018-09-28T20:04:25.000Z

## Abstract

We study the contextual linear bandit problem, a version of the standard stochastic multi-armed bandit (MAB) problem where a learner sequentially selects actions to maximize a reward which depends also on a user provided per-round context. Though the context is chosen arbitrarily or adversarially, the reward is assumed to be a stochastic function of a feature vector that encodes the context and selected action. Our goal is to devise private learners for the contextual linear bandit problem.   We first show that using the standard definition of differential privacy results in linear regret. So instead, we adopt the notion of joint differential privacy, where we assume that the action chosen on day $t$ is only revealed to user $t$ and thus needn't be kept private that day, only on following days. We give a general scheme converting the classic linear-UCB algorithm into a joint differentially private algorithm using the tree-based algorithm. We then apply either Gaussian noise or Wishart noise to achieve joint-differentially private algorithms and bound the resulting algorithms' regrets. In addition, we give the first lower bound on the additional regret any private algorithms for the MAB problem must incur.

## 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 Jester](<https://www.sota2.com/research/sota/contextual-bandits-on-jester.md>): Contextual Bandits; Jester; Non-private LinUCB Performance: 81.6.

- [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: 71.8.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1810.00068>)

[PDF](<https://arxiv.org/pdf/1810.00068.pdf>)