We study the regret in stochastic Multi-Armed Bandits (MAB) with multiple agents that communicate over an arbitrary connected communication graph. We show a near-optimal individual regret bound of $\tilde{O}(\sqrt{AT/m}+A)$, where $A$ is the number of actions, $T$ the time horizon, and $m$ the number of agents. In particular, assuming a sufficient number of agents, we achieve a regret bound of $\tilde{O}(A)$, which is independent of the sub-optimality gaps and the diameter of the communication graph. To the best of our knowledge, our study is the first to show an individual regret bound in cooperative stochastic MAB that is independent of the graph's diameter and applicable to non-fully-connected communication graphs.

翻译：我们研究了在任意连通通信图上进行通信的多智能体随机多臂老虎机（MAB）中的遗憾问题。我们展示了一个近乎最优的个体遗憾界 $\tilde{O}(\sqrt{AT/m}+A)$，其中 $A$ 是动作数量，$T$ 是时间范围，$m$ 是智能体数量。特别地，在假设有足够多智能体的情况下，我们得到了一个独立于次优间隙和通信图直径的遗憾界 $\tilde{O}(A)$。据我们所知，我们的研究首次在合作随机MAB中展示了一个独立于图直径且适用于非全连通通信图的个体遗憾界。