Fast column generation for atomic norm regularization

Marina Vinyes, Guillaume Obozinski
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:547-556, 2017.

Abstract

We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective Frank-Wolfe (FCFW) algorithm — which is most naturally reformulated as a column generation algorithm in the regularized case — can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the min-norm point algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-vinyes17a, title = {{Fast column generation for atomic norm regularization}}, author = {Vinyes, Marina and Obozinski, Guillaume}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {547--556}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/vinyes17a/vinyes17a.pdf}, url = {https://proceedings.mlr.press/v54/vinyes17a.html}, abstract = {We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective Frank-Wolfe (FCFW) algorithm — which is most naturally reformulated as a column generation algorithm in the regularized case — can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the min-norm point algorithm.} }
Endnote
%0 Conference Paper %T Fast column generation for atomic norm regularization %A Marina Vinyes %A Guillaume Obozinski %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-vinyes17a %I PMLR %P 547--556 %U https://proceedings.mlr.press/v54/vinyes17a.html %V 54 %X We consider optimization problems that consist in minimizing a quadratic function under an atomic norm regularization or constraint. In the line of work on conditional gradient algorithms, we show that the fully corrective Frank-Wolfe (FCFW) algorithm — which is most naturally reformulated as a column generation algorithm in the regularized case — can be made particularly efficient for difficult problems in this family by solving the simplicial or conical subproblems produced by FCFW using a special instance of a classical active set algorithm for quadratic programming that generalizes the min-norm point algorithm.
APA
Vinyes, M. & Obozinski, G.. (2017). Fast column generation for atomic norm regularization. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:547-556 Available from https://proceedings.mlr.press/v54/vinyes17a.html.

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