Related papers: Using Sinkhorn in the JKO scheme adds linear diffu…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the…

We introduce a deep neural network-based numerical method for solving kinetic Fokker Planck equations, including both linear and nonlinear cases. Building upon the conservative dissipative structure of Vlasov-type equations, we formulate a…

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…

Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can…

In this paper, we propose the optimal production transport model, which is an extension of the classical optimal transport model. We observe in economics, the production of the factories can always be adjusted within a certain range, while…

We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…

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…

This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…

This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). The algorithm is based on a recently introduced variational…

In transportation planning and development, transport network design problem seeks to optimize specific objectives (e.g. total travel time) through choosing among a given set of projects while keeping consumption of resources (e.g. budget)…

We study the Schr\"odinger-Bass problem, a one-parameter family of semimartingale optimal transport problems indexed by $\beta>0$, whose limiting regimes interpolate between the classical Schr\"odinger bridge, the Brenier-Strassen problem,…

We show that a solution of the optimal assignment problem can be obtained as the limit of the solution of an entropy maximization problem, as a deformation parameter tends to infinity. This allows us to apply entropy maximization algorithms…

We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr\"odinger potentials describing the density of the optimal…

Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance,…

We present a method to efficiently compute Wasserstein gradient flows. Our approach is based on a generalization of the back-and-forth method (BFM) introduced by Jacobs and L\'eger to solve optimal transport problems. We evolve the gradient…

The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…

We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valued Radon measure on the same set that describes a flow…

We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…

The problem of reconciling a prior probability law on paths with data was introduced by E. Schr\"odinger in 1931/32. It represents an early formulation of a maximum likelihood problem. This specific formulation can also be seen as the…