{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/general-single-loop-methods-for-bilevel","title":"Single-loop methods for bilevel parameter learning in inverse imaging","arxiv_id":"2408.08123","date":"2024-08-15","proceeding":null,"authors":["Ensio Suonperä","Tuomo Valkonen"],"abstract":"Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the process is costly. To reduce this cost, recently so-called single-loop approaches have been introduced. On each step of an outer optimisation method, they take just a single gradient step towards the solution of the inner problem. In this paper, we flexibilise the inner algorithm to include standard methods in inverse imaging. Moreover, as we have recently shown, significant performance improvements can be obtained in PDE-constrained optimisation by interweaving the steps of conventional iterative linear system solvers with the optimisation method. We now demonstrate how the adjoint equation in bilevel problems can also benefit from such interweaving. We evaluate the performance of our approach on identifying the deconvolution kernel for image deblurring, and the subsampling operator for magnetic resonance imaging (MRI).","url_abs":"https://arxiv.org/abs/2408.08123v2","url_pdf":"https://arxiv.org/pdf/2408.08123v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"general-single-loop-methods-for-bilevel","repo_url":"https://zenodo.org/record/15006162","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}