Complementary composite minimization, small gradients in general norms, and applications

Simple item page
dc.contributor.authorDiakonikolas, Jelena
dc.contributor.authorGuzman, Cristobal
dc.date.accessioned2025-01-20T17:10:21Z
dc.date.available2025-01-20T17:10:21Z
dc.date.issued2024
dc.description.abstractComposite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We introduce a new algorithmic framework for complementary composite minimization, where the objective function decouples into a (weakly) smooth and a uniformly convex term. This particular form of decoupling is pervasive in statistics and machine learning, due to its link to regularization. The main contributions of our work are summarized as follows. First, we introduce the problem of complementary composite minimization in general normed spaces; second, we provide a unified accelerated algorithmic framework to address broad classes of complementary composite minimization problems; and third, we prove that the algorithms resulting from our framework are near-optimal in most of the standard optimization settings. Additionally, we show that our algorithmic framework can be used to address the problem of making the gradients small in general normed spaces. As a concrete example, we obtain a nearly-optimal method for the standard l(1) (small gradients in the l(infinity) norm), essentially matching the bound of Nesterov (Optima Math Optim Soc Newsl 88:10-11, 2012) that was previously known only for the Euclidean setup. Finally, we show that our composite methods are broadly applicable to a number of regression and other classes of optimization problems, where regularization plays a key role. Our methods lead to complexity bounds that are either new or match the best existing ones.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s10107-023-02040-5
dc.identifier.eissn1436-4646
dc.identifier.issn0025-5610
dc.identifier.urihttps://doi.org/10.1007/s10107-023-02040-5
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/91102
dc.identifier.wosidWOS:001136803700001
dc.issue.numero1-2
dc.language.isoen
dc.pagina.final363
dc.pagina.inicio319
dc.revistaMathematical programming
dc.rightsacceso restringido
dc.subjectComposite minimization
dc.subjectGradient norm minimization
dc.subjectLinear convergence
dc.subjectRegression
dc.titleComplementary composite minimization, small gradients in general norms, and applications
dc.typeartículo
dc.volumen208
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Complementary composite minimization, small gradients.pdf
Size:
619.44 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Artículos de revistas