Decentralized Cooperative Stochastic Multi-armed Bandits

We study a decentralized cooperative stochastic multi-armed bandit problem with $K$ arms on a network of $N$ agents. In our model, the reward distribution of each arm is agent-independent. Each agent chooses iteratively one arm to play and then communicates to her neighbors. The aim is to minimize the total network regret. We design a fully decentralized algorithm that uses a running consensus procedure to compute, with some delay, accurate estimations of the average of rewards obtained by all the agents for each arm, and then uses an upper confidence bound algorithm that accounts for the delay and error of the estimations. We analyze the algorithm and up to a constant our regret bounds are better for all networks than other algorithms designed to solve the same problem. For some graphs, our regret bounds are significantly better.