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Pre-trained representation is one of the key elements in the success of modern deep learning. However, existing works on continual learning methods have mostly focused on learning models incrementally from scratch. In this paper, we explore…

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…

This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…

This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized…

In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in…

Real-world large-scale datasets are heteroskedastic and imbalanced -- labels have varying levels of uncertainty and label distributions are long-tailed. Heteroskedasticity and imbalance challenge deep learning algorithms due to the…

Regularization techniques are crucial to improving the generalization performance and training efficiency of deep neural networks. Many deep learning algorithms rely on weight decay, dropout, batch/layer normalization to converge faster and…

We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

Training deep neural networks is known to require a large number of training samples. However, in many applications only few training samples are available. In this work, we tackle the issue of training neural networks for classification…

Bilevel programming is one of the very active areas of research with many real-life applications in economics and engineering. Bilevel problems are hierarchical problems consisting of lower-level and upper-level problems, respectively. The…

In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained…

We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…

Deformable medical image registration is traditionally formulated as an optimization problem. While classical methods solve this problem iteratively, recent learning-based approaches use recurrent neural networks (RNNs) to mimic this…

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…

Deep learning models, including modern systems like large language models, are well known to offer unreliable estimates of the uncertainty of their decisions. In order to improve the quality of the confidence levels, also known as…