English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In various domains within imaging and data science, particularly whenaddressing tasks modeled utilizing the variational regularization approach,manually configuring regularization parameters presents a formidable challenge.The difficulty intensifies when employing regularizers involving a large numberof hyperparameters. To overcome this challenge, bilevel learning is employed tolearn suitable hyperparameters. However, due to the use of numerical solvers,the exact gradient with respect to the hyperparameters is unattainable,necessitating the use of methods relying on approximate gradients.State-of-the-art inexact methods a priori select a decreasing summable sequenceof the required accuracy and only assure convergence given a sufficiently smallfixed step size. Despite this, challenges persist in determining the Lipschitzconstant of the hypergradient and identifying an appropriate fixed step size.Conversely, computing exact function values is not feasible, impeding the useof line search. In this work, we introduce a provably convergent inexactbacktracking line search involving inexact function evaluations andhypergradients. We show convergence to a stationary point of the loss withrespect to hyperparameters. Additionally, we propose an algorithm to determinethe required accuracy dynamically. Our numerical experiments demonstrate theefficiency and feasibility of our approach for hyperparameter estimation invariational regularization problems, alongside its robustness in terms of theinitial accuracy and step size choices.

Dynamic Bilevel Learning with Inexact Line Search