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Projected Newton-type methods in machine learning
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.
@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}, slug = {6824}, author = {Schmidt, M. and Kim, D. and Sra, S.}, month_numeric = {12} }