Distributed Learning in Multi-Armed Bandit With Multiple Players

• Published in: IEEE transactions on signal processing Vol. 58; no. 11; pp. 5667 - 5681
• Main Authors: Liu, Keqin, Zhao, Qing
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Advertising; Applied sciences; Arm; Cognitive radio; Construction; Decentralized; decentralized multi-armed bandit; distributed learning; Exact sciences and technology; Exchanging; Information, signal and communications theory; Laboratories; Miscellaneous; multi-agent systems; Networks; Optimization; Permission; Players; Policies; Radio access networks; Radio networks; Searching; Signal processing; Social network services; Studies; system regret; TDF; Telecommunications and information theory; USA Councils; Web search; Web search and advertising; Lower bound; multi-agent systems; Logarithmic function; Transmission channel; Equity; Social network; Cognitive radio; decentralized multi-armed bandit; Learning; Web search and advertising; Multiagent system; Decentralized system; Time sharing system; Telecommunication system; Signal processing; distributed learning; system regret; Advertising; Information exchange; Radio communication; Software radio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2062509

We formulate and study a decentralized multi-armed 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.