AISTATS 2021poster21 citations
Iterative regularization for convex regularizers
Cesare Molinari, Mathurin Massias, Lorenzo Rosasco, Silvia Villa
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.
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. }
}