Decentralized Upper Confidence Bound Algorithms for Homogeneous Multi-Agent Multi-Armed Bandits

This article studies a decentralized homogeneous multiarmed bandit problem in a multiagent network. The problem is simultaneously solved by <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> agents assuming that they face a common set of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> arms and share the same arms' reward distributions. Each agent can receive information only from its neighbors, where the neighbor relationships among the agents are described by a fixed graph. Two fully decentralized upper confidence bound (UCB) algorithms are proposed for undirected graphs, respectively, based on the classic UCB1 algorithm and the state-of-the-art Kullback–Leibler upper confidence bound (KL-UCB) algorithm. The proposed decentralized UCB1 and KL-UCB algorithms permit each agent in the network to achieve a better logarithmic asymptotic regret than their single-agent counterparts, provided that the agent has at least one neighbor, and the more neighbors an agent has, the better regret it will have, meaning that the sum is more than its component parts. The same algorithm design framework is also extended to directed graphs through the design of a variant of the decentralized UCB1 algorithm, which outperforms the single-agent UCB1 algorithm.