{"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/inexact-derivative-free-optimization-for","title":"Inexact Derivative-Free Optimization for Bilevel Learning","arxiv_id":"2006.12674","date":"2020-06-23","proceeding":null,"authors":["Matthias J. Ehrhardt","Lindon Roberts"],"abstract":"Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to resolve this issue is to learn these parameters from data. While mathematically appealing this strategy leads to a nested optimization problem (known as bilevel optimization) which is computationally very difficult to handle. It is common when solving the upper-level problem to assume access to exact solutions of the lower-level problem, which is practically infeasible. In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require exact lower-level problem solutions, but instead assume access to approximate solutions with controllable accuracy, which is achievable in practice. We prove global convergence and a worstcase complexity bound for our approach. We test our proposed framework on ROFdenoising and learning MRI sampling patterns. Dynamically adjusting the lower-level accuracy yields learned parameters with similar reconstruction quality as highaccuracy evaluations but with dramatic reductions in computational work (up to 100 times faster in some cases).","url_abs":"https://arxiv.org/abs/2006.12674v2","url_pdf":"https://arxiv.org/pdf/2006.12674v2.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":"abstracts"},"code_links":[{"paper_slug":"inexact-derivative-free-optimization-for","repo_url":"https://github.com/lindonroberts/inexact_dfo_bilevel_learning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"bilevel-optimization","task_name":"Bilevel Optimization"},{"task_slug":"denoising","task_name":"Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.12674","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}