Multiplayer bandits without observing collision information

We study multiplayer stochastic multi-armed bandit problems in which the players cannot communicate, and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward. We consider two feedback models: a model in which the players can observe whether a collision has occurred, and a more difficult setup when no collision information is available. We give the first theoretical guarantees for the second model: an algorithm with a logarithmic regret, and an algorithm with a square-root regret type that does not depend on the gaps between the means. For the first model, we give the first square-root regret bounds that do not depend on the gaps. Building on these ideas, we also give an algorithm for reaching approximate Nash equilibria quickly in stochastic anti-coordination games.