Session S08 - Inverse Problems and Applications

Friday, July 23, 16:00 ~ 16:30 UTC-3

Bilevel learning for inverse problems

Juan Carlos De los Reyes

MODEMAT, Escuela Politécnica Nacional, Ecuador   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In recent years, novel optimization ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different quantities/functions of interest. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based on a training set is used. When confronted with inverse problems with nonsmooth regularizers, however, the bilevel optimization problem structure becomes quite involved to be analyzed, as classical nonlinear or bilevel programming results cannot be directly utilized. As a remedy, tools from nonsmooth variational analysis have to be employed to cope with the difficulties related with the lack of differentiability of the solution mapping or the failure of standard constraint qualifications. In this talk, I will discuss on the different challenges that these problems pose, and provide some analytical results of the bilevel problems, as well as solutions algorithms that may be devised based on the nonsmooth properties of the problems at hand.

Joint work with David Villacís (MODEMAT, Escuela Politécnica Nacional, Ecuador).

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