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We consider a cooperative multiplayer bandit learning problem where theplayers are only allowed to agree on a strategy beforehand, but cannotcommunicate during the learning process. In this problem, each playersimultaneously selects an action. Based on the actions selected by all players,the team of players receives a reward. The actions of all the players arecommonly observed. However, each player receives a noisy version of the rewardwhich cannot be shared with other players. Since players receive potentiallydifferent rewards, there is an asymmetry in the information used to selecttheir actions. In this paper, we provide an algorithm based on upper and lowerconfidence bounds that the players can use to select their optimal actionsdespite the asymmetry in the reward information. We show that this algorithmcan achieve logarithmic $O(\frac{\log T}{\Delta_{\bm{a}}})$ (gap-dependent)regret as well as $O(\sqrt{T\log T})$ (gap-independent) regret. This isasymptotically optimal in $T$. We also show that it performs empirically betterthan the current state of the art algorithm for this environment.

Optimal Cooperative Multiplayer Learning Bandits with Noisy Rewards and No Communication