Decentralized Upper Confidence Bound Algorithms for Homogeneous Multi-Agent Multi-Armed Bandits

TL;DR

This paper introduces decentralized UCB algorithms for multi-agent multi-armed bandits, enabling agents to collaboratively improve decision-making with limited local information in networked environments.

Contribution

It proposes new decentralized UCB algorithms for undirected and directed graphs, achieving better regret bounds than single-agent methods.

Findings

Decentralized UCB algorithms outperform single-agent counterparts in regret.

More neighbors lead to better regret performance for each agent.

The algorithms extend to directed graphs, maintaining improved regret.

Abstract

This paper studies a decentralized homogeneous multi-armed bandit problem in a multi-agent network. The problem is simultaneously solved by $N$ agents assuming they face a common set of $M$ arms and share the same arms' reward distributions. Each agent can receive information only from its neighbors, where the neighbor relationships among the agents are described by a fixed graph. Two fully decentralized upper confidence bound (UCB) algorithms are proposed for undirected graphs, respectively based on the classic algorithm and the state-of-the-art Kullback-Leibler upper confidence bound (KL-UCB) algorithm. The proposed decentralized UCB1 and KL-UCB algorithms permit each agent in the network to achieve a better logarithmic asymptotic regret than their single-agent counterparts, provided that the agent has at least one neighbor, and the more neighbors an agent has, the better regret it will have, meaning that the sum is more than its component parts. The same algorithm design framework is also extended to directed graphs through the design of a variant of the decentralized UCB1 algorithm, which outperforms the single-agent UCB1 algorithm.