Optimal Algorithms for Multiplayer Multi-Armed Bandits

The paper addresses various Multiplayer Multi-Armed Bandit (MMAB) problems, where M decision-makers, or players, collaborate to maximize their cumulative reward. We first investigate the MMAB problem where players selecting the same arms experience a collision (and are aware of it) and do not collect any reward. For this problem, we present DPE1 (Decentralized Parsimonious Exploration), a decentralized algorithm that achieves the same asymptotic regret as that obtained by an optimal centralized algorithm. DPE1 is simpler than the state-of-the-art algorithm SIC-MMAB Boursier and Pen-het (2019), and yet offers better performance guarantees. We then study the MMAB problem without collision, where players may select the same arm. Players sit on vertices of a graph, and in each round, they are able to send a message to their neighbours in the graph. We present DPE2, a simple and asymptotically optimal algorithm that outperforms the state-of-the-art algorithm DD-UCB Martinez-Rubio et al. (2019). Besides, under DPE2, the expected number of bits transmitted by the players in the graph is finite.