A Parallel algorithm for $\mathcal{X}$-Armed bandits

TL;DR

This paper introduces a distributed algorithm for $ ext{X}$-armed bandits that leverages multiple players to efficiently find the global maximum of an unknown function, significantly reducing computation time and communication rounds.

Contribution

The paper presents a novel anytime distributed $ ext{X}$-armed bandit algorithm with a unique search strategy suitable for large-scale, multi-player scenarios, achieving linear speedup and logarithmic communication complexity.

Findings

Algorithm is $m$ times faster than single-player methods.

Communication rounds are only logarithmic in $mn$.

Numerical results confirm effective multi-player utilization.

Abstract

The target of $\mathcal{X}$-armed bandit problem is to find the global maximum of an unknown stochastic function $f$, given a finite budget of $n$ evaluations. Recently, $\mathcal{X}$-armed bandits have been widely used in many situations. Many of these applications need to deal with large-scale data sets. To deal with these large-scale data sets, we study a distributed setting of $\mathcal{X}$-armed bandits, where $m$ players collaborate to find the maximum of the unknown function. We develop a novel anytime distributed $\mathcal{X}$-armed bandit algorithm. Compared with prior work on $\mathcal{X}$-armed bandits, our algorithm uses a quite different searching strategy so as to fit distributed learning scenarios. Our theoretical analysis shows that our distributed algorithm is $m$ times faster than the classical single-player algorithm. Moreover, the number of communication rounds of our algorithm is only logarithmic in $mn$. The numerical results show that our method can make effective use of every players to minimize the loss. Thus, our distributed approach is attractive and useful.