We consider the cooperative multi-player version of the stochastic multi-armed bandit problem. We study the regime where the players cannot communicate but have access to shared randomness. In prior work by the first two authors, a strategy for this regime was constructed for two players and three arms, with regret $\tilde{O}(\sqrt{T})$, and with no collisions at all between the players (with very high probability). In this paper we show that these properties (near-optimal regret and no collisions at all) are achievable for any number of players and arms. At a high level, the previous strategy heavily relied on a $2$-dimensional geometric intuition that was difficult to generalize in higher dimensions, while here we take a more combinatorial route to build the new strategy.

中文翻译：

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合作随机多人多臂强盗：既不沟通也不冲突的最优遗憾

我们考虑随机多臂老虎机问题的合作多人版本。我们研究了玩家无法交流但可以访问共享随机性的机制。在前两位作者的先前工作中，该机制的策略是为两个玩家和三个手臂构建的，遗憾的是 $\tilde{O}(\sqrt{T})$，并且玩家之间根本没有碰撞（概率非常高）。在本文中，我们展示了这些属性（接近最佳的遗憾和根本没有碰撞）对于任何数量的玩家和手臂都是可以实现的。在较高的层面上，之前的策略严重依赖于 $2$ 维的几何直觉，在更高维度上难以泛化，而在这里我们采用更组合的路线来构建新策略。