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Techniques for gradient based bilevel optimization with nonsmooth lower level problems

Peter Ochs, R. Ranftl, Thomas Brox, T. Pock
Journal of Mathematical Imaging and Vision, 56(2): 175-194, Oct 2016
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Abstract: We propose techniques for approximating bilevel optimization problems with non-smooth and non-unique lower level problems. The key is the substitution of the lower level minimization problem with an iterative algorithm that is guaranteed to converge to a minimizer of the problem. Using suitable non-linear proximal distance functions, the update mappings of such an iterative algorithm can be differentiable, notwithstanding the fact that the minimization problem is non-smooth. This technique for smoothly approximating the solution map of the lower level problem raises several questions that are discussed in this paper.

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BibTex references

@Article{OB16,
  author       = "P. Ochs and R. Ranftl and T. Brox and T. Pock",
  title        = "Techniques for gradient based bilevel optimization with nonsmooth lower level problems",
  journal      = "Journal of Mathematical Imaging and Vision",
  number       = "2",
  volume       = "56",
  pages        = "175-194",
  month        = "Oct",
  year         = "2016",
  url          = "http://lmb.informatik.uni-freiburg.de//Publications/2016/OB16"
}

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