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

04/28/2019

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by   Sébastien Bubeck, et al.

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We consider the non-stochastic version of the (cooperative) multi-player multi-armed bandit problem. The model assumes no communication at all between the players, and furthermore when two (or more) players select the same action this results in a maximal loss. We prove the first √(T)-type regret guarantee for this problem, under the feedback model where collisions are announced to the colliding players. Such a bound was not known even for the simpler stochastic version. We also prove the first sublinear guarantee for the feedback model where collision information is not available, namely T^1-1/2m where m is the number of players.