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

Etienne Boursier (1) , Emilie Kaufmann (2, 3, 4, 5) , Abbas Mehrabian (6) , Vianney Perchet (7, 8)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
2 CNRS - Centre National de la Recherche Scientifique
3 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
4 SEQUEL - Sequential Learning
5 Scool - Scool
6 McGill University = Université McGill [Montréal, Canada]
7 Criteo [Paris]
8 ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique

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 and efficient algorithm that combines the idea of leveraging forced collisions for implicit communication and that of performing matching eliminations. We present a finite-time analysis of our algorithm, giving the first sublinear minimax regret bound for this problem, and prove that if the optimal assignment of players to arms is unique, our algorithm attains the optimal O(ln(T )) regret, solving an open question raised at NeurIPS 2018 by Bistritz and Leshem (2018).

Mots clés: Distributed Learning; Multi-armed bandit; Combinatorial semi-bandits

Domaines: Machine Learning [stat.ML]

Etienne Boursier, Emilie Kaufmann, Abbas Mehrabian, Vianney Perchet. A Practical Algorithm for Multiplayer Bandits when Arm Means Vary Among Players. AISTATS 2020 - 23rd International Conference on Artificial Intelligence and Statistics, Aug 2020, Palermo, Italy. ⟨hal-02006069v3⟩