| Title: |
Derivative-free stochastic bilevel optimization for inverse problems |
| Authors: |
Staudigl, Mathias; Weissmann, Simon; van Leeuwen, Tristan; Sub Mathematical Modeling; Mathematical Modeling |
| Publication Year: |
2026 |
| Subject Terms: |
Data-driven design; Derivative-free optimization; Gaussian smoothing; Inverse problems; Control and Optimization; Computational Mathematics; Applied Mathematics |
| Description: |
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and investigate their generalization properties when confronted with unseen data. This approach dictates a statistical approach to inverse problems, calling for stochastic optimization methods. In order to learn model and regularisation parameters simultaneously, we develop in this paper a stochastic bilevel optimization approach in which the lower level problem represents a variational reconstruction method formulated as a convex non-smooth optimization problem, depending on the observed sample. The upper level problem represents the learning task of the regularisation parameters. Combining the lower level and the upper level problem leads to a stochastic non-smooth and non-convex optimization problem, for which standard gradient-based methods are not straightforward to implement. Instead, we develop a unified and flexible methodology, building on a derivative-free approach, which allows us to solve the bilevel optimization problem only with samples of the objective function values. We perform a complete complexity analysis of this scheme. Numerical results on signal denoising and experimental design demonstrate the computational efficiency and the generalization properties of our method. |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
English |
| ISSN: |
0926-6003 |
| Relation: |
https://dspace.library.uu.nl/handle/1874/479315 |
| Availability: |
https://dspace.library.uu.nl/handle/1874/479315 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.9D56846F |
| Database: |
BASE |