Order-Optimal Regret in Distributed Kernel Bandits using Uniform Sampling with Shared Randomness

arXiv:2402.13182v1 Announce Type: new
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 …

abstract agent agents aim arxiv cs.dc cs.lg distributed function information kernel lies queries query randomness sampling space stat.ml through type uniform