Communication-Efficient Collaborative Heterogeneous Bandits in Networks

The multi-agent multi-armed bandit problem has been studied extensively due to its ubiquity in many real-life applications, such as online recommendation systems and wireless networking. We consider the setting where agents should minimize their group regret while collaborating over a given graph via some communication protocol and where each agent is given a different set of arms. Previous literature on this problem only considered one of the two desired features separately: agents with the same arm set communicate over a general graph, or agents with different arm sets communicate over a fully connected graph. In this work, we introduce a more general problem setting that encompasses all the desired features. For this novel setting, we first provide a rigorous regret analysis for the standard flooding protocol combined with the UCB policy. Then, to mitigate the issue of high communication costs incurred by flooding, we propose a new protocol called Flooding with Absorption (FWA). We provide a theoretical analysis of the regret bound and intuitions on the advantages of using FWA over flooding. Lastly, we verify empirically that using FWA leads to significantly lower communication costs despite minimal regret performance loss compared to flooding.