Proximal boosting: aggregating weak learners to minimize non-differentiable losses

TL;DR

This paper introduces proximal boosting, a new method for aggregating weak learners to minimize non-differentiable losses, offering improved convergence and accuracy over traditional gradient boosting.

Contribution

It develops a novel proximal boosting algorithm based on the proximal point method, with a residual variant for better error control, and provides theoretical convergence guarantees.

Findings

Proximal boosting converges faster than gradient boosting.

Proximal boosting achieves higher prediction accuracy.

Numerical experiments confirm the theoretical advantages.

Abstract

Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm, when the empirical risk to minimize is not differentiable, in order to introduce a novel boosting approach, called proximal boosting. It comes with a companion algorithm inspired by [1] and called residual proximal boosting, which is aimed at better controlling the approximation error. Theoretical convergence is proved for these two procedures under different hypotheses on the empirical risk and advantages of leveraging proximal methods for boosting are illustrated by numerical experiments on simulated and real-world data. In particular, we exhibit a favorable comparison over gradient boosting regarding convergence rate and prediction accuracy.