相关论文: Regularized Optimal Transport is Ground Cost Adver…

Learning policies from fixed offline datasets is a key challenge to scale up reinforcement learning (RL) algorithms towards practical applications. This is often because off-policy RL algorithms suffer from distributional shift, due to…

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…

We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…

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…

Deep neural networks, particularly in vision tasks, are notably susceptible to adversarial perturbations. To overcome this challenge, developing a robust classifier is crucial. In light of the recent advancements in the robustness of…

This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…

This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…

This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…

This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean $\ell_2$-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn--Knopp algorithm, Accelerated Gradient…

In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…

Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures $P$ and $Q$ is a problem fraught with computational and statistical challenges. A promising approach lies in using the dual potential functions obtained when…

Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…

Computing optimal transport (OT) distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. In this paper, we study the problem of approximating the general OT distance…

Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…

This paper addresses the problem of robust option pricing within the framework of Vectorial Martingale Optimal Transport (VMOT). We investigate the geometry of VMOT solutions for $N$-period market models and demonstrate that, when the…

In this note, we derive upper-bounds on the statistical estimation rates of unbalanced optimal transport (UOT) maps for the quadratic cost. Our work relies on the stability of the semi-dual formulation of optimal transport (OT) extended to…

Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while…

The use of optimal transport (OT) distances, and in particular entropic-regularised OT distances, is an increasingly popular evaluation metric in many areas of machine learning and data science. Their use has largely been driven by the…