Iterative regularization for low complexity regularizers
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211_2023_1390_ReferencePDF.pdf
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Author(s)
Molinari, Cesare
Massias, Mathurin
Rosasco, Lorenzo
Villa, Silvia
Date Issued
February 10, 2024
Journal
Numerische Mathematik
Publisher
Springer Berlin Heidelberg
Citation
Molinari, C., Massias, M., Rosasco, L. et al. Iterative regularization for low complexity regularizers. Numer. Math. 156, 641–689 (2024).
Version
Author's final manuscript
Abstract
Iterative regularization exploits the implicit bias of optimization algorithms to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in modern machine learning, where it provides both a new perspective on algorithms analysis, and significant speed-ups compared to explicit regularization. In this work, we propose and study the first iterative regularization procedure with explicit computational steps able to handle biases described by non smooth and non strongly convex functionals, prominent in low-complexity regularization. Our approach is based on a primal-dual algorithm of which we analyze convergence and stability properties, even in the case where the original problem is unfeasible. The general results are illustrated considering the special case of sparse recovery with the ℓ 1 penalty. Our theoretical results are complemented by experiments showing the computational benefits of our approach.
MIT Department
Center for Brains, Minds, and Machines
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00211-023-01390-8
