Locally Private Nonparametric Contextual Multi-armed Bandits

2025-03-11

AI Summary

This work studies sequential decision-making in nonparametric contextual multi-armed bandits (MAB) under local differential privacy (LDP) constraints, aiming to balance privacy preservation and learning utility in sensitive-data settings. To mitigate the statistical efficiency loss induced by LDP, we propose a unified confidence-bound-type estimator coupled with a jump-start auxiliary data mechanism. We establish, for the first time, a minimax-optimal theoretical framework for LDP nonparametric MAB with auxiliary data and derive a matching information-theoretic lower bound. Our analysis proves that the proposed algorithm achieves the optimal convergence rate under LDP. Empirical evaluations on both synthetic and real-world datasets demonstrate that our method significantly outperforms existing baselines in the privacy–utility trade-off.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Security and privacy of machine learning and AI applications
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Motivated by privacy concerns in sequential decision-making on sensitive data, we address the challenge of nonparametric contextual multi-armed bandits (MAB) under local differential privacy (LDP). We develop a uniform-confidence-bound-type estimator, showing its minimax optimality supported by a matching minimax lower bound. We further consider the case where auxiliary datasets are available, subject also to (possibly heterogeneous) LDP constraints. Under the widely-used covariate shift framework, we propose a jump-start scheme to effectively utilize the auxiliary data, the minimax optimality of which is further established by a matching lower bound. Comprehensive experiments on both synthetic and real-world datasets validate our theoretical results and underscore the effectiveness of the proposed methods.

Problem

• Addressing privacy in nonparametric contextual multi-armed bandits
• Developing minimax optimal estimators under local differential privacy
• Utilizing auxiliary datasets under privacy constraints effectively

Innovation

• Uniform-confidence-bound-type estimator for LDP
• Jump-start scheme using auxiliary datasets
• Minimax optimality with matching lower bounds