Locally Private Nonparametric Contextual Multi-armed Bandits
This work addresses privacy-sensitive sequential decision-making problems, such as in healthcare or finance, by providing a locally private framework, though it is incremental as it builds on existing bandit and privacy methods.
The paper tackled the problem of nonparametric contextual multi-armed bandits under local differential privacy to address privacy concerns in sequential decision-making, achieving minimax optimality with matching lower bounds and validating results through experiments on synthetic and real-world datasets.
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.