165. General single-loop splitting methods for bilevel optimization
Invited abstract in session FC-5: Recent advances in bilevel optimization III, stream Bilevel optimization: strategies for complex decision-making.
Friday, 11:25 - 12:40Room: M:N
Authors (first author is the speaker)
| 1. | Ensio Suonperä
|
| Mathematics and statistics, University of Helsinki | |
| 2. | Tuomo Valkonen
|
| Escuela Politécnica Nacional |
Abstract
Bilevel problems have been traditionally solved through either treating the inner problem as a constraint, and solving the resulting Karush--Kuhn--Tucker conditions using a Newton-type solver; or by trivialising the inner problem to its solution mapping. These approaches are difficult to scale to large problems. The latter approach in principle requires near-exact solution of the inner problem for each outer iterate. Recently, intermediate approaches have surfaced that solve the inner problem to a low precision and still obtain some form of convergence. In this talk, we discuss the linear convergence of methods based on taking interleaved steps of proximal-type methods on both the inner and outer problem. We demonstrate numerical performance on imaging applications. Such bilevel learning problems have a large scale, as the dimension depends on the size of the images, which can be in the order of millions of pixels, the size of the training set, and the number of parameters to be learned.
Keywords
- Multilevel optimization
- Optimization for learning and data analysis
- Large- and Huge-scale optimization
Status: accepted
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