Distributed Exploration in Multi-Armed Bandits

TL;DR

This paper investigates how multiple players can collaborate in multi-armed bandit problems to improve learning efficiency, revealing a tradeoff between communication and speed-up, and demonstrating near-optimal parallelization.

Contribution

It introduces algorithms and bounds for distributed exploration in multi-armed bandits, showing a sqrt(k) speed-up with minimal communication and an approach for k-fold speed-up with limited communication.

Findings

Single communication allows sqrt(k) speed-up.

Lower bound matches the sqrt(k) speed-up limit.

Algorithm achieves k-fold speed-up with logarithmic communication.

Abstract

We study exploration in Multi-Armed Bandits in a setting where $k$ players collaborate in order to identify an $\epsilon$-optimal arm. Our motivation comes from recent employment of bandit algorithms in computationally intensive, large-scale applications. Our results demonstrate a non-trivial tradeoff between the number of arm pulls required by each of the players, and the amount of communication between them. In particular, our main result shows that by allowing the $k$ players to communicate only once, they are able to learn $\sqrt{k}$ times faster than a single player. That is, distributing learning to $k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement this result with a lower bound showing this is in general the best possible. On the other extreme, we present an algorithm that achieves the ideal factor $k$ speed-up in learning performance, with communication only logarithmic in $1/\epsilon$.