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We consider the non-stochastic version of the (cooperative) multi-playermulti-armed bandit problem. The model assumes no communication at all betweenthe players, and furthermore when two (or more) players select the same actionthis results in a maximal loss. We prove the first $\sqrt{T}$-type regretguarantee for this problem, under the feedback model where collisions areannounced to the colliding players. Such a bound was not known even for thesimpler stochastic version. We also prove the first sublinear guarantee for thefeedback model where collision information is not available, namely$T^{1-\frac{1}{2m}}$ where $m$ is the number of players.

Non-Stochastic Multi-Player Multi-Armed Bandits: Optimal Rate With Collision Information, Sublinear Without