A Practical Algorithm for Multiplayer Bandits when Arm Means Vary Among Players
This solves an open problem in multi-agent learning for scenarios like wireless networks, with incremental improvements in algorithm design.
The paper tackles the multiplayer bandit problem with heterogeneous arm means and no communication, where collisions yield zero reward, by proposing a new algorithm that achieves the first sublinear minimax regret bound and optimal O(ln(T)) regret under unique optimal assignments.
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.