在隐私保护下解决非参数上下文多臂赌博机问题，提升数据安全与决策效率。
Locally Private Nonparametric Contextual Multi-armed Bandits
- 设计基于统一置信区间估计的隐私保护方法，保证理论最优性。
- 在辅助数据存在时，提出跳转启动策略，显著提升学习效率。
- 适用于医疗、金融等敏感数据场景，兼顾隐私与性能。
针对敏感数据序列决策中的隐私问题，本文研究在局部差分隐私（LDP）约束下的非参数上下文多臂赌博机（MAB）问题。提出一种统一置信界类型的估计器，并通过匹配的极小极大下界证明其最小极大最优性。进一步考虑存在辅助数据的情况，且辅助数据也受（可能异质的）LDP约束。在常用的协变量偏移框架下，提出一种跳转启动机制以有效利用辅助数据，其最小极大最优性亦由匹配下界支持。在合成与真实数据集上的全面实验验证了理论结果，并凸显所提方法的有效性。
原文摘要 · Abstract (English)
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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