Computational Mathematics and Scientific Computing Seminar

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Bilevel learning for inverse problems

Speaker: Juan Carlos De los Reyes, Escuela Politécnica Nacional

Location: Warren Weaver Hall 1302

Date: Sept. 16, 2022, 10 a.m.

Synopsis:

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 or nonlinear operators, however, the bilevel optimization problem structure becomes quite involved to be analyzed, as classical nonlinear or bilevel programming results cannot be directly utilized. In this talk, I will discuss on the different challenges that these problems pose, and provide some analytical results as well as a numerical solution strategy.