  We study a distributed decision-making problem in which multiple agents face
the same multi-armed bandit (MAB), and each agent makes sequential choices
among arms to maximize its own individual reward. The agents cooperate by
sharing their estimates over a fixed communication graph. We consider an
unconstrained reward model in which two or more agents can choose the same arm
and collect independent rewards. And we consider a constrained reward model in
which agents that choose the same arm at the same time receive no reward. We
design a dynamic, consensus-based, distributed estimation algorithm for
cooperative estimation of mean rewards at each arm. We leverage the estimates
from this algorithm to develop two distributed algorithms: coop-UCB2 and
coop-UCB2-selective-learning, for the unconstrained and constrained reward
models, respectively. We show that both algorithms achieve group performance
close to the performance of a centralized fusion center. Further, we
investigate the influence of the communication graph structure on performance.
We propose a novel graph explore-exploit index that predicts the relative
performance of groups in terms of the communication graph, and we propose a
novel nodal explore-exploit centrality index that predicts the relative
performance of agents in terms of the agent locations in the communication
graph.
