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Despite the significant interests and many progresses in decentralizedmulti-player multi-armed bandits (MP-MAB) problems in recent years, the regretgap to the natural centralized lower bound in the heterogeneous MP-MAB settingremains open. In this paper, we propose BEACON -- Batched Exploration withAdaptive COmmunicatioN -- that closes this gap. BEACON accomplishes this goalwith novel contributions in implicit communication and efficient exploration.For the former, we propose a novel adaptive differential communication (ADC)design that significantly improves the implicit communication efficiency. Forthe latter, a carefully crafted batched exploration scheme is developed toenable incorporation of the combinatorial upper confidence bound (CUCB)principle. We then generalize the existing linear-reward MP-MAB problems, wherethe system reward is always the sum of individually collected rewards, to a newMP-MAB problem where the system reward is a general (nonlinear) function ofindividual rewards. We extend BEACON to solve this problem and prove alogarithmic regret. BEACON bridges the algorithm design and regret analysis ofcombinatorial MAB (CMAB) and MP-MAB, two largely disjointed areas in MAB, andthe results in this paper suggest that this previously ignored connection isworth further investigation.

Heterogeneous Multi-player Multi-armed Bandits: Closing the Gap and Generalization