Proximal boosting and its acceleration

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 to introduce a novel boosting approach, called proximal boosting. Besides being motivated by non-differentiable optimization, the proposed algorithm benefits from Nesterov's acceleration in the same way as gradient boosting [Biau et al., 2018]. This leads to a variant, called accelerated proximal boosting. 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

From Proximal Point Method to Nesterov's Acceleration

The proximal point method (PPM) is a fundamental method in optimization that is often used as a building block for fast optimization algorithms. In this work, building on a recent work by Defazio (2019), we provide a complete understanding of Nesterov's accelerated gradient method (AGM) by establishing quantitative and analytical connections between PPM and AGM. The main observation in this paper is that AGM is in fact equal to a simple approximation of PPM, which results in an elementary derivation of the mysterious updates of AGM as well as its step sizes. This connection also leads to a conceptually simple analysis of AGM based on the standard analysis of PPM. This view naturally extends to the strongly convex case and also motivates other accelerated methods for practically relevant settings.Comment: 14 pages; Section 4 updated; Remark 5 added; comments would be appreciated