New Algorithms for Multiplayer Bandits when Arm Means Vary Among Players
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We study multiplayer stochastic multi-armed bandit problems in which the players cannot communicate,and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward.Moreover, we assume each arm has a different mean for each player. Let T denote the number of rounds.An algorithm with regret O(( T)^2+κ) for any constant κ was recently presented by Bistritz and Leshem (NeurIPS 2018), who left the existence of an algorithm with O( T) regret as an open question. In this paper, we provide an affirmative answer to this question in the case when there is a unique optimal assignment of players to arms. For the general case we present an algorithm with expected regret O(( T)^1+κ), for any κ>0.
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