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The Vehicle Routing Problem is about optimizing the routes of vehicles to meet the needs of customers at specific locations. The route graph consists of depots on several levels and customer positions. Several optimization methods have been…

Artificial Intelligence · Computer Science 2024-09-18 László Kovács , Ali Jlidi

The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…

Optimization and Control · Mathematics 2022-10-25 Nazarii Tupitsa , Pavel Dvurechensky , Darina Dvinskikh , Alexander Gasnikov

Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several…

Machine Learning · Statistics 2021-03-09 Meyer Scetbon , Marco Cuturi , Gabriel Peyré

We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…

Probability · Mathematics 2017-08-04 Florent Bekerman

Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…

Machine Learning · Computer Science 2025-04-04 Mete Kemertas , Amir-massoud Farahmand , Allan D. Jepson

Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…

Optimization and Control · Mathematics 2022-06-28 Zixuan Cang , Qing Nie , Yanxiang Zhao

In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drastically increasing the computational cost of sampling and evaluation of a lower bound on the likelihood.…

Machine Learning · Computer Science 2020-02-19 Chin-Wei Huang , Laurent Dinh , Aaron Courville

Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…

We propose a novel algorithm for offline reinforcement learning using optimal transport. Typically, in offline reinforcement learning, the data is provided by various experts and some of them can be sub-optimal. To extract an efficient…

Machine Learning · Computer Science 2024-10-21 Arip Asadulaev , Rostislav Korst , Alexander Korotin , Vage Egiazarian , Andrey Filchenkov , Evgeny Burnaev

Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…

Machine Learning · Computer Science 2025-05-07 Koshi Oishi , Yota Hashizume , Tomohiko Jimbo , Hirotaka Kaji , Kenji Kashima

The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…

Optimization and Control · Mathematics 2025-09-03 Alberto González-Sanz , Michel Groppe , Axel Munk

Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…

Machine Learning · Computer Science 2022-03-09 Nathaniel Lahn , Sharath Raghvendra , Kaiyi Zhang

Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…

Statistics Theory · Mathematics 2022-06-08 Ziv Goldfeld , Kengo Kato , Gabriel Rioux , Ritwik Sadhu

Training a Deep Neural Network (DNN) from scratch requires a large amount of labeled data. For a classification task where only small amount of training data is available, a common solution is to perform fine-tuning on a DNN which is…

Computer Vision and Pattern Recognition · Computer Science 2017-09-12 Ying Lu , Liming Chen , Alexandre Saidi

Recently, the trend of incorporating differentiable algorithms into deep learning architectures arose in machine learning research, as the fusion of neural layers and algorithmic layers has been beneficial for handling combinatorial data,…

Machine Learning · Computer Science 2022-02-04 Alberto Archetti , Marco Cannici , Matteo Matteucci

Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well…

Machine Learning · Statistics 2022-06-22 Wei-Ting Chiu , Pei Wang , Patrick Shafto

It is often desired that ordinal regression models yield unimodal predictions. However, in many recent works this characteristic is either absent, or implemented using soft targets, which do not guarantee unimodal outputs at inference. In…

Machine Learning · Statistics 2021-11-19 Uri Shaham , Igal Zaidman , Jonathan Svirsky

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

Statistics Theory · Mathematics 2021-02-18 Lucas de Lara , Alberto González-Sanz , Jean-Michel Loubes

We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…

Statistics Theory · Mathematics 2022-03-03 Bernard Bercu , Jérémie Bigot , Sébastien Gadat , Emilia Siviero

This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…