Locally Private Nonparametric Contextual Multi-armed Bandits

Yuheng Ma; Feiyu Jiang; Zifeng Zhao; Hanfang Yang; Yi Yu

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arXiv · 2503.08098

Locally Private Nonparametric Contextual Multi-armed Bandits

Yuheng Ma·Feiyu Jiang·Zifeng Zhao·Hanfang Yang·Yi Yu

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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.

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BibTeX RIS

Yuheng Ma, Feiyu Jiang, Zifeng Zhao, Hanfang Yang, Yi Yu. 2025-03-11. Locally Private Nonparametric Contextual Multi-armed Bandits. https://arxiv.org/abs/2503.08098

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