Locally Private Nonparametric Contextual Multi-armed Bandits

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.

@article{ma2025_2503.08098,
  title={ Locally Private Nonparametric Contextual Multi-armed Bandits },
  author={ Yuheng Ma and Feiyu Jiang and Zifeng Zhao and Hanfang Yang and Yi Yu },
  journal={arXiv preprint arXiv:2503.08098},
  year={ 2025 }
}