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

TL;DR

This paper introduces a new algorithm for multiplayer bandit problems with heterogeneous arm means, achieving optimal regret bounds and enabling implicit communication through collisions.

Contribution

It presents the first sublinear minimax regret bound for heterogeneous multiplayer bandits and demonstrates optimal regret when the best assignment is unique.

Findings

Achieves $O( abla ext{ln}(T))$ regret in the heterogeneous setting.

Uses collision-based implicit communication for coordination.

Solves an open problem from NeurIPS 2018.

Abstract

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.