Optimal Parallelization of Boosting

TL;DR

This paper characterizes the true parallel complexity of Boosting algorithms, providing tight bounds and a matching parallel algorithm that nearly achieves optimal performance across various tradeoffs.

Contribution

It establishes improved lower bounds and introduces a parallel Boosting algorithm that closely matches these bounds, closing the gap in the parallel complexity landscape.

Findings

Derived tight lower bounds on Boosting parallel complexity.

Developed a parallel Boosting algorithm matching these bounds.

Achieved near-optimal performance across the entire tradeoff spectrum.

Abstract

Recent works on the parallel complexity of Boosting have established strong lower bounds on the tradeoff between the number of training rounds $p$ and the total parallel work per round $t$. These works have also presented highly non-trivial parallel algorithms that shed light on different regions of this tradeoff. Despite these advancements, a significant gap persists between the theoretical lower bounds and the performance of these algorithms across much of the tradeoff space. In this work, we essentially close this gap by providing both improved lower bounds on the parallel complexity of weak-to-strong learners, and a parallel Boosting algorithm whose performance matches these bounds across the entire $p$ vs.~$t$ compromise spectrum, up to logarithmic factors. Ultimately, this work settles the true parallel complexity of Boosting algorithms that are nearly sample-optimal.