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We study a decentralized cooperative multi-agent multi-armed bandit problemwith $K$ arms and $N$ agents connected over a network. In our model, each arm'sreward distribution is same for all agents, and rewards are drawn independentlyacross agents and over time steps. In each round, agents choose an arm to playand subsequently send a message to their neighbors. The goal is to minimizecumulative regret averaged over the entire network. We propose a decentralizedBayesian multi-armed bandit framework that extends single-agent Bayesian banditalgorithms to the decentralized setting. Specifically, we study an informationassimilation algorithm that can be combined with existing Bayesian algorithms,and using this, we propose a decentralized Thompson Sampling algorithm anddecentralized Bayes-UCB algorithm. We analyze the decentralized ThompsonSampling algorithm under Bernoulli rewards and establish a problem-dependentupper bound on the cumulative regret. We show that regret incurred scaleslogarithmically over the time horizon with constants that match those of anoptimal centralized agent with access to all observations across the network.Our analysis also characterizes the cumulative regret in terms of the networkstructure. Through extensive numerical studies, we show that our extensions ofThompson Sampling and Bayes-UCB incur lesser cumulative regret than thestate-of-art algorithms inspired by the Upper Confidence Bound algorithm. Weimplement our proposed decentralized Thompson Sampling under gossip protocol,and over time-varying networks, where each communication link has a fixedprobability of failure.

Bayesian Algorithms for Decentralized Stochastic Bandits