Curvature-Exploiting Acceleration of Elastic Net Computations
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.
BibTeX
@InProceedings{pmlr-v97-mai19a,
title = {Curvature-Exploiting Acceleration of Elastic Net Computations},
author = {Mai, Vien and Johansson, Mikael},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {4294--4303},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/mai19a/mai19a.pdf},
url = {https://proceedings.mlr.press/v97/mai19a.html},
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.}
}