We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected (quasi-)Newton method. This method, while conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are more scalable, namely, two-metric projection and inexact projection methods. Finally, we show how to apply the Newton-type framework to handle non-smooth objectives. Examples are provided throughout the chapter to illustrate machine learning applications of our framework.
| Author(s): | Schmidt, M. and Kim, D. and Sra, S. |
| Links: | |
| Book Title: | Optimization for Machine Learning |
| Pages: | 305-330 |
| Year: | 2011 |
| Month: | December |
| Day: | 0 |
| Editors: | Sra, S., Nowozin, S. and Wright, S. J. |
| Publisher: | MIT Press |
| BibTeX Type: | Book Chapter (inbook) |
| Address: | Cambridge, MA, USA |
| Electronic Archiving: | grant_archive |
| ISBN: | 978-0-262-01646-9 |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
BibTeX
@inbook{6824,
title = {Projected Newton-type methods in machine learning},
booktitle = {Optimization for Machine Learning},
abstract = {We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected (quasi-)Newton method. This method, while conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are more scalable, namely, two-metric projection and inexact
projection methods. Finally, we show how to apply the Newton-type framework to handle non-smooth objectives. Examples are provided throughout the chapter to illustrate machine learning applications of our framework.},
pages = {305-330},
editors = {Sra, S., Nowozin, S. and Wright, S. J.},
publisher = {MIT Press},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Cambridge, MA, USA},
month = dec,
year = {2011},
author = {Schmidt, M. and Kim, D. and Sra, S.},
month_numeric = {12}
}