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We consider the cooperative multi-player version of the stochasticmulti-armed bandit problem. We study the regime where the players cannotcommunicate but have access to shared randomness. In prior work by the firsttwo authors, a strategy for this regime was constructed for two players andthree arms, with regret $\tilde{O}(\sqrt{T})$, and with no collisions at allbetween the players (with very high probability). In this paper we show thatthese properties (near-optimal regret and no collisions at all) are achievablefor any number of players and arms. At a high level, the previous strategyheavily relied on a $2$-dimensional geometric intuition that was difficult togeneralize in higher dimensions, while here we take a more combinatorial routeto build the new strategy.

Cooperative and Stochastic Multi-Player Multi-Armed Bandit: Optimal Regret With Neither Communication Nor Collisions