An Option and Agent Selection Policy with Logarithmic Regret for Multi Agent Multi Armed Bandit Problems on Random Graphs.

Existing studies of the Multi Agent Multi Armed Bandit (MAMAB) problem, with the exception of a very few, consider the case where the agents observe their neighbors according to a static network graph. They also mostly rely on a running consensus for the estimation of the option rewards. Two of the exceptions consider a problem where agents observe instantaneous rewards and actions of their neighbors through an iid ER graph process based communication strategy. In this paper we propose a UCB based option allocation rule that guarantees logarithmic regret even if the graph depends on the history of choices made by the agents. The paper also proposes a novel communication strategy that significantly outperforms the iid ER graph based communication strategy. In both the ER graph and the dependent graph strategy, the regret is shown to depend on the connectivity of the graph in a particularly interesting way where there exists an optimal connectivity of the graph that is less than the full connectivity of the graph.