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We study the cooperative asynchronous multi-agent multi-armed bandits problem, where each agent's active (arm pulling) decision rounds are asynchronous. That is, in each round, only a subset of agents is active to pull arms, and this subset is unknown and time-varying. We consider two models of multi-agent cooperation, fully distributed and leader-coordinated, and propose algorithms for both models that attain near-optimal regret and communications bounds, both of which are almost as good as their synchronous counterparts. The fully distributed algorithm relies on a novel communication policy consisting of accuracy adaptive and on-demand components, and successive arm elimination for decision-making. For leader-coordinated algorithms, a single leader explores arms and recommends them to other agents (followers) to exploit. As agents' active rounds are unknown, a competent leader must be chosen dynamically. We propose a variant of the Tsallis-INF algorithm with low switches to choose such a leader sequence. Lastly, we report numerical simulations of our new asynchronous algorithms with other known baselines. 

In this paper, we study the multi-scale expert problem, where the rewards of different experts vary in different reward ranges. The performance of existing algorithms for the multi-scale expert problem degrades linearly proportional to the maximum reward range of any expert or the best expert and does not capture the non-uniform heterogeneity in the reward ranges among experts. In this work, we propose learning algorithms that construct a hierarchical tree structure based on the heterogeneity of the reward range of experts and then determine differentiated learning rates based on the reward upper bounds and cumulative empirical feedback over time. We then characterize the regret of the proposed algorithms as a function of non-uniform reward ranges and show that their regrets outperform prior algorithms when the rewards of experts exhibit non-uniform heterogeneity in different ranges. Last, our numerical experiments verify our algorithms' efficiency compared to previous algorithms.