Order-Optimal Regret in Distributed Kernel Bandits using Uniform Sampling with Shared Randomness
Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Pavlovic, Nikola, Salgia, Sudeep, Zhao, Qing
Institutions: Cornell University, Carnegie Mellon University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4392019618