Locally Private Nonparametric Contextual Multi-armed Bandits with Transfer Learning

Motivated by privacy concerns in sequential decision-making on sensitive data, we address the challenging problem of nonparametric contextual multi-armed bandits (MAB) under local differential privacy (LDP). Via a novelly designed LDP-compatible confidence bound, we propose an algorithm that achieves near-optimal regret performance, whose optimality is further supported by a first-seen minimax lower bound. We further consider the case of private transfer learning where auxiliary datasets are available, subject also to (heterogeneous) LDP constraints. Under the widely-used covariate shift framework, we propose a jump-start scheme, accompanied with a reweighted LDP-compatible estimator and confidence bound, which effectively combine information from heterogeneous auxiliary data. The minimax optimality of the algorithm 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.