Related papers: MinMax Methods for Optimal Transport and Beyond: R…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

A problem that arises in drawings of transportation networks is to minimize the number of crossings between different transportation lines. While this can be done efficiently under specific constraints, not all solutions are visually…

Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and…

We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in…

We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…

In this work, we present a novel tool for reconstructing networks from corrupted images. The reconstructed network is the result of a minimization problem that has a misfit term with respect to the observed data, and a physics-based…

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…

In this work, we consider learning over multitask graphs, where each agent aims to estimate its own parameter vector. Although agents seek distinct objectives, collaboration among them can be beneficial in scenarios where relationships…

We propose to tackle the problem of understanding the effect of regularization in Sinkhorn algotihms. In the case of Gaussian distributions we provide a closed form for the regularized optimal transport which enables to provide a better…

We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the…

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of…

Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance…

Learning conditional distributions is challenging because the desired outcome is not a single distribution but multiple distributions that correspond to multiple instances of the covariates. We introduce a novel neural entropic optimal…

We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is $c$-convex, then the source has a canonical foliation whose…

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of…

We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for…

Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…