Related papers: Learning to Transport with Neural Networks

Planning a network of public transit routes is a challenging optimization problem. Metaheuristic algorithms search through the space of possible transit networks by applying heuristics that randomly alter routes in a network. Existing…

Modern communication networks are increasingly equipped with in-network computational capabilities and services. Routing in such networks is significantly more complicated than the traditional routing. A legitimate route for a flow not only…

In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…

This short review aims to make the reader familiar with state-of-the-art works relating to planning, scheduling and learning. First, we study state-of-the-art planning algorithms. We give a brief introduction of neural networks. Then we…

Neural networks have been achieving high generalization performance on many tasks despite being highly over-parameterized. Since classical statistical learning theory struggles to explain this behavior, much effort has recently been focused…

We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…

Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…

Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to…

Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network based optimal transport map solver has gained great attention in…

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…

This thesis explores the benefits machine learning algorithms can bring to online planning and scheduling for autonomous vehicles in off-road situations. Mainly, we focus on typical problems of interest which include computing itineraries…

We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-agent systems. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of…

This paper introduces the first statistically consistent estimator of the optimal transport map between two probability distributions, based on neural networks. Building on theoretical and practical advances in the field of Lipschitz neural…

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…

We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

Recent observations have advanced our understanding of the neural network optimization landscape, revealing the existence of (1) paths of high accuracy containing diverse solutions and (2) wider minima offering improved performance.…