Distributed Cooperative Decision-Making in Multiarmed Bandits: Frequentist and Bayesian Algorithms

TL;DR

This paper extends frequentist and Bayesian algorithms for multi-armed bandits to a distributed multi-agent setting, analyzing how communication networks influence collective decision-making performance.

Contribution

It introduces cooperative distributed algorithms for multi-agent MAB problems, leveraging consensus methods and analyzing their asymptotic performance and network effects.

Findings

Algorithms asymptotically match centralized performance.

Performance depends on the communication graph structure.

Rigorous performance guarantees are provided.

Abstract

We study distributed cooperative decision-making under the explore-exploit tradeoff in the multiarmed bandit (MAB) problem. We extend the state-of-the-art frequentist and Bayesian algorithms for single-agent MAB problems to cooperative distributed algorithms for multi-agent MAB problems in which agents communicate according to a fixed network graph. We rely on a running consensus algorithm for each agent's estimation of mean rewards from its own rewards and the estimated rewards of its neighbors. We prove the performance of these algorithms and show that they asymptotically recover the performance of a centralized agent. Further, we rigorously characterize the influence of the communication graph structure on the decision-making performance of the group.