We consider distributed kernel bandits where $N$ agents aim to collaboratively maximize an unknown reward function that lies in a reproducing kernel Hilbert space. Each agent sequentially queries the function to obtain noisy observations at the query points. Agents can share information through a central server, with the objective of minimizing regret that is accumulating over time $T$ and aggregating over agents. We develop the first algorithm that achieves the optimal regret order (as defined by centralized learning) with a communication cost that is sublinear in both $N$ and $T$. The key features of the proposed algorithm are the uniform exploration at the local agents and shared randomness with the central server. Working together with the sparse approximation of the GP model, these two key components make it possible to preserve the learning rate of the centralized setting at a diminishing rate of communication.

我们提出了第一个算法，它以次线性的通信成本实现了最佳的（以集中式学习定义的）遗憾顺序，通过局部智能的均匀探索和与中央服务器共享随机性这两个关键组成部分与GP模型的稀疏近似共同作用，能够以递减的通信速率保持集中设置的学习速率。

分布式内核赌博机中使用共享随机采样的最佳订单遗憾