Distributed learning in multi-armed bandit with multiple players

We formulate and study a decentralized multi-armed bandit (MAB) problem. There are distributed players competing for independent arms. Each arm, when played, offers i.i.d. reward according to a distribution with an unknown parameter. At each time, each player chooses one arm to play without exchanging observations or any information with other players. Players choosing the same arm collide, and, depending on the collision model, either no one receives reward or the colliding players share the reward in an arbitrary way. We show that the minimum system regret of the decentralized MAB grows with time at the same logarithmic order as in the centralized counterpart where players act collectively as a single entity by exchanging observations and making decisions jointly. A decentralized policy is constructed to achieve this optimal order while ensuring fairness among players and without assuming any pre-agreement or information exchange among players. Based on a time-division fair sharing (...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Keqin Liu, Qing Zhao
• Keywords: Artificial Intelligence, Decentralized Multi-armed Bandit, Order Optimality, Policy, TSP 2010