Multiplayer bandits have recently been extensively studied because of their application to cognitive radio networks. While the literature mostly considers synchronous players, radio networks (e.g. for IoT) tend to have asynchronous devices. This motivates the harder, asynchronous multiplayer bandits problem, which was first tackled with an explore-then-commit (ETC) algorithm (see Dakdouk, 2022), with a regret upper-bound in $\mathcal{O}(T^{\frac{2}{3}})$. Before even considering decentralization, understanding the centralized case was still a challenge as it was unknown whether getting a regret smaller than $\Omega(T^{\frac{2}{3}})$ was possible. We answer positively this question, as a natural extension of UCB exhibits a $\mathcal{O}(\sqrt{T\log(T)})$ minimax regret. More importantly, we introduce Cautious Greedy, a centralized algorithm that yields constant instance-dependent regret if the optimal policy assigns at least one player on each arm (a situation that is proved to occur when arm means are close enough). Otherwise, its regret increases as the sum of $\log(T)$ over some sub-optimality gaps. We provide lower bounds showing that Cautious Greedy is optimal in the data-dependent terms. Therefore, we set up a strong baseline for asynchronous multiplayer bandits and suggest that learning the optimal policy in this problem might be easier than thought, at least with centralization.

研究了多人赌注问题在异步设备中的实际应用和中心化算法的最小化后悔值，介绍了谨慎贪婪算法并证明其在数据依赖术语方面是最优的。

异步多人赌博机中的常数或对数遗憾