A Practical Algorithm for Multiplayer Bandits when Arm Means Vary Among Players

To appear in AISTATS 2020

Authors: E. Boursier, E. Kaufmann, A. Mehrabian and V. Perchet

We study a multiplayer stochastic multi-armed bandit problem in which players cannot communicate, and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward. We consider the challenging heterogeneous setting, in which different arms may have different means for different players, and propose a new, efficient algorithm that combines the idea of leveraging forced collisions for implicit communication and that of performing matching eliminations. We give a finite-time analysis of our algorithm, bounding its regret by $O((\log T)^{1+\kappa})$ for any fixed $\kappa>0$. If the optimal assignment of players to arms is unique, we further show that it attains the optimal $O(\log(T))$ regret, solving an open question raised at NeurIPS 2018.

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