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arXiv · 1602.07080

Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems

Peter Ochs·René Ranftl·Thomas Brox·Thomas Pock
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Abstract

We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer 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.

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Peter Ochs, René Ranftl, Thomas Brox, Thomas Pock. 2016-02-23. Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems. https://arxiv.org/abs/1602.07080

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