Techniques for Gradient-Based Bilevel Optimization with Non-smooth Lower Level Problems
By Peter Ochs, René Ranftl, Thomas Brox, Thomas Pock. 2016
52 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Numerical Analysis
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In Computational Theory and Mathematics
In Management Science and Operations Research
- Nathan Kallus
- Masatoshi Uehara
- Andrew Bennett
- Susan Athey
- Stefan Wager
- Angela Zhou
- Guido W. Imbens
- Maria Dimakopoulou
In Numerical Analysis
Citations in the corpus
- Balanced Policy Evaluation and Learning (2017, methodology): “This is a limitation of the current optimization algorithm that we hope to improve on in the future using specialized methods for bilevel optimization [4, 32, 37].”