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Related papers: On Convex Duality in Linear Inverse Problems

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We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

Optimization and Control · Mathematics 2020-12-29 Sheheryar Mehmood , Peter Ochs

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Computational Engineering, Finance, and Science · Computer Science 2018-12-04 Ivan Dokmanić , Joan Bruna , Stéphane Mallat , Maarten de Hoop

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…

Optimization and Control · Mathematics 2023-11-03 Angelia Nedich , Tatiana Tatarenko

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

Optimization and Control · Mathematics 2018-12-27 Jan Kuske , Paul Swoboda , Stefania Petra

Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…

Optimization and Control · Mathematics 2019-04-05 Jozef Kratica , Vladimir Filipovic , Dragan Matic , Aleksandar Kartelj

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

Computational Physics · Physics 2021-10-22 Feng Wang , Alberto Eljarrat , Johannes Müller , Trond Henninen , Erni Rolf , Christoph Koch

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…

Machine Learning · Computer Science 2020-09-16 Adam Ibrahim , Waïss Azizian , Gauthier Gidel , Ioannis Mitliagkas

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

Machine Learning · Computer Science 2023-07-04 Litu Rout , Negin Raoof , Giannis Daras , Constantine Caramanis , Alexandros G. Dimakis , Sanjay Shakkottai

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…

Machine Learning · Computer Science 2025-01-08 Han Shen , Quan Xiao , Tianyi Chen

It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being…

Robotics · Computer Science 2017-02-01 Yasir Latif , Guoquan Huang , John Leonard , Jose Neira

Inverse Reinforcement Learning (IRL) is a powerful set of techniques for imitation learning that aims to learn a reward function that rationalizes expert demonstrations. Unfortunately, traditional IRL methods suffer from a computational…

Machine Learning · Computer Science 2024-01-31 Gokul Swamy , Sanjiban Choudhury , J. Andrew Bagnell , Zhiwei Steven Wu

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

Optimization and Control · Mathematics 2025-03-25 Xinwei Liu , Vladimir Dvorkin

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

Computer Vision and Pattern Recognition · Computer Science 2024-09-19 Sai Bharath Chandra Gutha , Ricardo Vinuesa , Hossein Azizpour

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

Machine Learning · Computer Science 2024-02-08 Moshe Eliasof , Eldad Haber , Eran Treister

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…

Optimization and Control · Mathematics 2017-02-22 Peyman Mohajerin Esfahani , Tobias Sutter , Daniel Kuhn , John Lygeros

The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…

Optimization and Control · Mathematics 2018-05-29 Fedor S. Stonyakin , Mohammad S. Alkousa , Alexey N. Stepanov , Maxim A. Barinov

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…

Computer Vision and Pattern Recognition · Computer Science 2023-09-19 Huayu Wang , Chen Luo , Taofeng Xie , Qiyu Jin , Guoqing Chen , Zhuo-Xu Cui , Dong Liang

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

Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…

Machine Learning · Computer Science 2020-10-26 Jonathan Wenger , Philipp Hennig