Mathematical Optimization for Data Science Group, Saarland University

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Mathematical Optimization for Data Science Group

Department of Mathematics and Computer Science, Saarland University, Germany

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Bilevel Optimization with Nonsmooth Lower Level Problems

P. Ochs, R. Ranftl, T. Brox and T. Pock

Abstract:
We consider a bilevel optimization approach for parameter learning in nonsmooth variational models. Existing approaches solve this problem by applying implicit differentiation to a sufficiently smooth approximation of the nondifferentiable lower level problem. We propose an alternative method based on differentiating the iterations of a nonlinear primal--dual algorithm. Our method computes exact (sub)gradients and can be applied also in the nonsmooth setting. We show preliminary results for the case of multi-label image segmentation.



pdf	Bibtex	Publisher's link

Citation:
P. Ochs, R. Ranftl, T. Brox, T. Pock:
Bilevel Optimization with Nonsmooth Lower Level Problems.

In J.-F. Aujol, M. Nikolova, N. Papadakis (Eds.): International Conference on Scale Space and Variational Methods in Computer Vision (SSVM). Lecture Notes in Computer Science, Vol. 9087, 654-665, Springer, 2015. (Best Paper Award)

Bibtex:
@inproceedings{ORBP15, title = {Bilevel Optimization with Nonsmooth Lower Level Problems}, author = {P. Ochs and R. Ranftl and T. Brox and T. Pock}, year = {2015}, editor = {J.-F. Aujol and M. Nikolova and N. Papadakis}, booktitle = {International Conference on Scale Space and Variational Methods in Computer Vision (SSVM)}, series = {Lecture Notes in Computer Science}, publisher = {Springer}, volume = {9087}, pages = {654--665} }

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