Related papers: Orlicz-space regularization for optimal transport …
We study the semi-discrete formulation of one-dimensional partial optimal transport with quadratic cost, where a probability density is partially transported to a finite sum of Dirac masses of smaller total mass. This problem arises…
For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper/lower continuous capacities and to prove the cyclic monotonicity of the supports of optimal supermodular plans. As in the probabilistic…
The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
We study the Optimal Transport problem for laws of random measures in the Kantorovich-Wasserstein space $\mathcal{P}_2(\mathcal{P}_2(\mathrm{H}))$, associated with a Hilbert space $\mathrm{H}$ (with finite or infinite dimension) and for the…
A precise characterization of the extremal points of sublevel sets of nonsmooth penalties provides both detailed information about minimizers, and optimality conditions in general classes of minimization problems involving them. Moreover,…
Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
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…
We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…
We present a new approach for Neural Optimal Transport (NOT) training procedure, capable of accurately and efficiently estimating optimal transportation plan via specific regularization on dual Kantorovich potentials. The main bottleneck of…
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…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
Many results in probability (most famously, Strassen's theorem on stochastic domination), characterize some relationship between probability distributions in terms of the existence of a particular structured coupling between them. Optimal…