Iterative regularization for convex regularizers

Cesare Molinari, Mathurin Massias, Lorenzo Rosasco, Silvia Villa
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1684-1692, 2021.

Abstract

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence of worst case deterministic noise. As a main example, we specialize and illustrate the results for the problem of robust sparse recovery. Key to our analysis is a combination of ideas from regularization theory and optimization in the presence of errors. Theoretical results are complemented by experiments showing that state-of-the-art performances are achieved with considerable computational speed-ups.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-molinari21a, title = { Iterative regularization for convex regularizers }, author = {Molinari, Cesare and Massias, Mathurin and Rosasco, Lorenzo and Villa, Silvia}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1684--1692}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/molinari21a/molinari21a.pdf}, url = {https://proceedings.mlr.press/v130/molinari21a.html}, abstract = { We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence of worst case deterministic noise. As a main example, we specialize and illustrate the results for the problem of robust sparse recovery. Key to our analysis is a combination of ideas from regularization theory and optimization in the presence of errors. Theoretical results are complemented by experiments showing that state-of-the-art performances are achieved with considerable computational speed-ups. } }
Endnote
%0 Conference Paper %T Iterative regularization for convex regularizers %A Cesare Molinari %A Mathurin Massias %A Lorenzo Rosasco %A Silvia Villa %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-molinari21a %I PMLR %P 1684--1692 %U https://proceedings.mlr.press/v130/molinari21a.html %V 130 %X We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence of worst case deterministic noise. As a main example, we specialize and illustrate the results for the problem of robust sparse recovery. Key to our analysis is a combination of ideas from regularization theory and optimization in the presence of errors. Theoretical results are complemented by experiments showing that state-of-the-art performances are achieved with considerable computational speed-ups.
APA
Molinari, C., Massias, M., Rosasco, L. & Villa, S.. (2021). Iterative regularization for convex regularizers . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1684-1692 Available from https://proceedings.mlr.press/v130/molinari21a.html.

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