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Convergence of a Piggyback-style method for the differentiation of solutions of standard saddle-point problems

Bogensperger, Lea; Chambolle, Antonin; Pock, Thomas (2022), Convergence of a Piggyback-style method for the differentiation of solutions of standard saddle-point problems. https://basepub.dauphine.psl.eu/handle/123456789/22785

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03516542
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
22
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Author(s)
Bogensperger, Lea
Institute for Computer Graphics and Vision [Graz] [ICG]
Chambolle, Antonin cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Pock, Thomas
Institute for Computer Graphics and Vision [Graz] [ICG]
Abstract (EN)
We analyse a "piggyback"-style method for computing the derivative of a loss which depends on the solution of a convex-concave saddle point problems, with respect to the bilinear term. We attempt to derive guarantees for the algorithm under minimal regularity assumption on the functions. Our final convergence results include possibly nonsmooth objectives. We illustrate the versatility of the proposed piggyback algorithm by learning optimized shearlet transforms, which are a class of popular sparsifying transforms in the field of imaging.
Subjects / Keywords
First-order methods; saddle-point problems; differentiation; adjoint methods; piggyback algorithm; learning