  Cooperative multi-agent decision making involves a group of agents
cooperatively solving learning problems while communicating over a network with
delays. In this paper, we consider the kernelised contextual bandit problem,
where the reward obtained by an agent is an arbitrary linear function of the
contexts' images in the related reproducing kernel Hilbert space (RKHS), and a
group of agents must cooperate to collectively solve their unique decision
problems. For this problem, we propose \textsc{Coop-KernelUCB}, an algorithm
that provides near-optimal bounds on the per-agent regret, and is both
computationally and communicatively efficient. For special cases of the
cooperative problem, we also provide variants of \textsc{Coop-KernelUCB} that
provides optimal per-agent regret. In addition, our algorithm generalizes
several existing results in the multi-agent bandit setting. Finally, on a
series of both synthetic and real-world multi-agent network benchmarks, we
demonstrate that our algorithm significantly outperforms existing benchmarks.
