Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems
Optimization and Control
2016-04-27 v2
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.
Cite
@article{arxiv.1602.07080,
title = {Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems},
author = {Peter Ochs and René Ranftl and Thomas Brox and Thomas Pock},
journal= {arXiv preprint arXiv:1602.07080},
year = {2016}
}