Competing for Shareable Arms in Multi-Player Multi-Armed Bandits
This addresses competition for limited resources in multi-agent learning, but it is incremental as it builds on existing MPMAB frameworks with a novel sharing assumption.
The paper tackles the problem of designing individualized competing policies for selfish agents in a multi-player multi-armed bandit setting with shareable rewards, proposing the SMAA approach that achieves good regret guarantees and robustness against deviations.
Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel Selfish MPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.