In this paper, we investigate a novel problem of building contextual bandits in the vertical federated setting, i.e., contextual information is vertically distributed over different departments. This problem remains largely unexplored in the research community. To this end, we carefully design a customized encryption scheme named orthogonal matrix-based mask mechanism(O3M) for encrypting local contextual information while avoiding expensive conventional cryptographic techniques. We further apply the mechanism to two commonly-used bandit algorithms, LinUCB and LinTS, and instantiate two practical protocols for online recommendation under the vertical federated setting. The proposed protocols can perfectly recover the service quality of centralized bandit algorithms while achieving a satisfactory runtime efficiency, which is theoretically proved and analyzed in this paper. By conducting extensive experiments on both synthetic and real-world datasets, we show the superiority of the proposed method in terms of privacy protection and recommendation performance.

翻译：在本文中,我们调查了在纵向联合环境下建立背景强盗的新问题,即背景信息是垂直分布于不同部门的。这个问题在研究界基本上尚未探讨。为此,我们仔细设计了一个定制的加密方案,名为正方形矩阵基底掩码机制(O3M),用于加密本地背景信息,同时避免昂贵的常规加密技术。我们进一步对两种常用的盗匪算法(LinUCB和LINTS)应用了这一机制,并在纵向联合设置下即时为在线建议设定了两个实用协议。拟议的协议可以完全恢复集中式土匪算法的服务质量,同时实现令人满意的运行效率,本文从理论上加以验证和分析。通过对合成和现实世界数据集进行广泛的实验,我们展示了拟议方法在隐私保护和建议性表现方面的优势。