# Curvature-Exploiting Acceleration of Elastic Net Computations

## TL;DR

This paper presents a second-order optimization method for the elastic net that leverages curvature information to achieve faster convergence, especially on ill-conditioned datasets, with strong theoretical guarantees and practical benefits.

## Contribution

It introduces a novel curvature-exploiting technique for elastic net optimization, combining second-order information with variance reduction and momentum acceleration.

## Key findings

- Achieves faster run times than first-order methods.
- Demonstrates significant practical improvements on ill-conditioned data.
- Provides theoretical guarantees for the proposed method.

## Abstract

This paper introduces an efficient second-order method for solving the elastic net problem. Its key innovation is a computationally efficient technique for injecting curvature information in the optimization process which admits a strong theoretical performance guarantee. In particular, we show improved run time over popular first-order methods and quantify the speed-up in terms of statistical measures of the data matrix. The improved time complexity is the result of an extensive exploitation of the problem structure and a careful combination of second-order information, variance reduction techniques, and momentum acceleration. Beside theoretical speed-up, experimental results demonstrate great practical performance benefits of curvature information, especially for ill-conditioned data sets.