Order-Optimal Regret in Distributed Kernel Bandits using Uniform Sampling with Shared Randomness
This addresses the challenge of efficient collaboration in multi-agent systems for applications like sensor networks, though it is incremental as it builds on existing kernel bandit methods.
The paper tackles the problem of distributed kernel bandits where multiple agents collaborate to maximize an unknown reward function, achieving the first algorithm with optimal regret order and sublinear communication cost in both the number of agents and time.
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.