Corrupt Bandits for Preserving Local Privacy

TL;DR

This paper introduces a new corrupted bandit model motivated by privacy in recommender systems, providing theoretical regret bounds, privacy guarantees, and experimental validation for algorithms designed to operate under reward corruption.

Contribution

It develops the first regret bounds for corrupted bandits, proposes new algorithms with privacy considerations, and analyzes the trade-off between privacy and learning performance.

Findings

Regret bounds are established for corrupted bandit algorithms.

Privacy guarantees are achieved through specific corruption parameters.

Experimental results validate the theoretical analysis and algorithm performance.

Abstract

We study a variant of the stochastic multi-armed bandit (MAB) problem in which the rewards are corrupted. In this framework, motivated by privacy preservation in online recommender systems, the goal is to maximize the sum of the (unobserved) rewards, based on the observation of transformation of these rewards through a stochastic corruption process with known parameters. We provide a lower bound on the expected regret of any bandit algorithm in this corrupted setting. We devise a frequentist algorithm, KLUCB-CF, and a Bayesian algorithm, TS-CF and give upper bounds on their regret. We also provide the appropriate corruption parameters to guarantee a desired level of local privacy and analyze how this impacts the regret. Finally, we present some experimental results that confirm our analysis.