Bilevel Optimization with Nonsmooth Lower Level Problems

Peter Ochs, R. Ranftl, Thomas Brox, T. Pock

International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), Springer, LNCS, Vol.9087: 654--665, 2015

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.

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@InProceedings{OB15a,
  author       = "P. Ochs and R. Ranftl and T. Brox and T. Pock",
  title        = "Bilevel Optimization with Nonsmooth Lower Level Problems",
  booktitle    = "International Conference on Scale Space and Variational Methods in Computer Vision (SSVM)",
  series       = "Lecture Notes in Computer Science",
  volume       = "9087",
  pages        = "654--665",
  month        = " ",
  year         = "2015",
  editor       = "J.-F. Aujol, M. Nikolova, N. Papadakis",
  publisher    = "Springer",
  note         = "Awarded the SSVM 2015 Best Paper Award",
  url          = "http://lmbweb.informatik.uni-freiburg.de/Publications/2015/OB15a"
}

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