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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, SIAM Journal on Mathematics of Data Science, 4, 3. 10.1137/21M1455887

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
SIAM Journal on Mathematics of Data Science
Volume
4
Number
3
Published in
Paris
Publication identifier
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Author(s)
Bogensperger, Lea
Institute for Computer Graphics and Vision [Graz] [ICG]
Chambolle, Antonin
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