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Deep neural networks are a promising approach towards multi-task learning because of their capability to leverage knowledge across domains and learn general purpose representations. Nevertheless, they can fail to live up to these promises…

Machine Learning · Computer Science 2019-12-17 Mihai Suteu , Yike Guo

Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…

Machine Learning · Computer Science 2017-11-10 Hyeonwoo Noh , Tackgeun You , Jonghwan Mun , Bohyung Han

Exploring machine learning techniques for addressing vehicle routing problems has attracted considerable research attention. To achieve decent and efficient solutions, existing deep models for vehicle routing problems are typically trained…

Machine Learning · Computer Science 2025-10-21 Jingwen Li , Zhiguang Cao , Yaoxin Wu , Tang Liu

Image denoising is a classical problem in low level computer vision. Model-based optimization methods and deep learning approaches have been the two main strategies for solving the problem. Model-based optimization methods are flexible for…

Computer Vision and Pattern Recognition · Computer Science 2018-12-31 Chang Liu , Zhaowei Shang , Anyong Qin

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with…

Machine Learning · Computer Science 2026-01-08 Ray Zirui Zhang , Christopher E. Miles , Xiaohui Xie , John S. Lowengrub

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…

Computer Vision and Pattern Recognition · Computer Science 2017-07-11 Marco Loog , François Lauze

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Robotics · Computer Science 2023-09-19 Mohamad Qadri , Zachary Manchester , Michael Kaess

In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…

Optimization and Control · Mathematics 2022-03-29 Camilo Garcia Trillos , Nicolas Garcia Trillos

There is a significant performance gap between Binary Neural Networks (BNNs) and floating point Deep Neural Networks (DNNs). We propose to improve the binary training method, by introducing a new regularization function that encourages…

Machine Learning · Computer Science 2020-04-22 Sajad Darabi , Mouloud Belbahri , Matthieu Courbariaux , Vahid Partovi Nia

Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…

Machine Learning · Computer Science 2026-04-23 Xuelin Zhang , Peipei Yuan

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

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

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…

Optimization and Control · Mathematics 2017-05-09 Ankur Sinha , Zhichao Lu , Kalyanmoy Deb , Pekka Malo

The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems often exhibit non-uniqueness and ill-posedness, resulting…

Numerical Analysis · Mathematics 2024-10-21 Markus Haltmeier , Richard Kowar , Markus Tiefenthaler

Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Siddharth Prabhu , Srinivas Rangarajan , Mayuresh Kothare

Deep Reinforcement Learning (Deep RL) has been receiving increasingly more attention thanks to its encouraging performance on a variety of control tasks. Yet, conventional regularization techniques in training neural networks (e.g., $L_2$…

Machine Learning · Computer Science 2021-11-30 Zhuang Liu , Xuanlin Li , Bingyi Kang , Trevor Darrell

Designing learning systems which are invariant to certain data transformations is critical in machine learning. Practitioners can typically enforce a desired invariance on the trained model through the choice of a network architecture, e.g.…

Machine Learning · Computer Science 2022-10-26 Cédric Rommel , Thomas Moreau , Alexandre Gramfort

Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…

Systems and Control · Electrical Eng. & Systems 2025-12-30 Sampath Kumar Mulagaleti , Alberto Bemporad

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a…

Optimization and Control · Mathematics 2025-07-08 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt