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A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…

Analysis of PDEs · Mathematics 2019-03-19 Pan Liu

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

Optimization and Control · Mathematics 2026-02-06 Mattia Solla , Johannes O. Royset

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an…

Optimization and Control · Mathematics 2020-02-13 J. C. De los Reyes , C. -B. Schönlieb , T. Valkonen

Data augmentation is a key practice in machine learning for improving generalization performance. However, finding the best data augmentation hyperparameters requires domain knowledge or a computationally demanding search. We address this…

Computer Vision and Pattern Recognition · Computer Science 2020-11-11 Saypraseuth Mounsaveng , Issam Laradji , Ismail Ben Ayed , David Vazquez , Marco Pedersoli

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…

Optimization and Control · Mathematics 2024-11-28 Mathias Staudigl , Simon Weissmann , Tristan van Leeuwen

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…

Optimization and Control · Mathematics 2024-07-25 Bo Zhou , Ruiwei Jiang , Siqian Shen

We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…

Optimization and Control · Mathematics 2018-09-27 Mostafa Amini , Farzad Yousefian

We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse,…

Machine Learning · Computer Science 2022-09-13 Breno Serrano , Stefan Minner , Maximilian Schiffer , Thibaut Vidal

Enhancing images in low-light scenes is a challenging but widely concerned task in the computer vision. The mainstream learning-based methods mainly acquire the enhanced model by learning the data distribution from the specific scenes,…

Computer Vision and Pattern Recognition · Computer Science 2023-06-05 Long Ma , Dian Jin , Nan An , Jinyuan Liu , Xin Fan , Risheng Liu

We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…

Optimization and Control · Mathematics 2021-07-20 Juan Carlos De los Reyes , David Villacís

This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…

Optimization and Control · Mathematics 2025-11-06 Dhaval Pujara , Ankur Sinha

A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…

Optimization and Control · Mathematics 2018-12-05 Gernot Holler , Karl Kunisch , Richard C. Barnard

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…

Machine Learning · Statistics 2018-07-04 Luca Franceschi , Paolo Frasconi , Saverio Salzo , Riccardo Grazzi , Massimilano Pontil

In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…

Numerical Analysis · Mathematics 2022-11-15 Valerio Pagliari , Kostas Papafitsoros , Bogdan Raiţă , Andreas Vikelis

Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…

Optimization and Control · Mathematics 2018-09-27 Harshal Kaushik , Farzad Yousefian

A novel class of semi-norms, generalising the notion of the isotropic total variation $TV_{2}$ and the an-isotropic total variation $TV_{1}$ is introduced. A supervised learning method via bilevel optimisation is proposed for the…

Analysis of PDEs · Mathematics 2019-03-29 Pan Liu , Carola-Bibiane Schönlieb

Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another…

Machine Learning · Computer Science 2023-07-11 Can Chen , Xi Chen , Chen Ma , Zixuan Liu , Xue Liu

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Optimization and Control · Mathematics 2024-11-05 Andi Han , Bamdev Mishra , Pratik Jawanpuria , Akiko Takeda

In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…

Optimization and Control · Mathematics 2026-04-03 Hang Xie , Xuewen Li , Peili Li , Qiuyu Wang

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

Optimization and Control · Mathematics 2021-04-20 Geunyeong Byeon , Pascal Van Hentenryck