Finite-time Analysis of the Multiarmed Bandit Problem
Machine Learning
Opportunistic spectrum access with multiple users: learning under competition
INFOCOM'10 Proceedings of the 29th conference on Information communications
Opportunistic transmission scheduling with resource-sharing constraints in wireless networks
IEEE Journal on Selected Areas in Communications
IEEE/ACM Transactions on Networking (TON)
Push the limit of wireless network capacity: a tale of cognitive and coexistence
Proceedings of the 1st ACM workshop on Cognitive radio architectures for broadband
| Hi-index | 35.68 |
We formulate and study a decentralized multiarmed bandit (MAB) problem. There are M distributed players competing for N 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 (TDFS) of the M best arms, the proposed policy is constructed and its order optimality is proven under a general reward model. Furthermore, the basic structure of the TDFS policy can be used with any order-optimal single-player policy to achieve order optimality in the decentralized setting. We also establish a lower bound on the system regret for a general class of decentralized polices, to which the proposed policy belongs. This problem finds potential applications in cognitive radio networks, multi-channel communication systems, multi-agent systems, web search and advertising, and social networks.