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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 introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the…
In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…
We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…
Using the recently developed Sinkhorn algorithm for approximating the Wasserstein distance between probability distributions represented by Monte Carlo samples, we demonstrate exponential filter stability of two commonly used nonlinear…
Entropic regularization provides a simple way to approximate linear programs whose constraints split into two or more tractable blocks. The resulting objectives are amenable to cyclic Kullback-Leibler (KL) Bregman projections, with…
We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable…
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 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…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
Sinkhorn divergence is a measure of dissimilarity between two probability measures. It is obtained through adding an entropic regularization term to Kantorovich's optimal transport problem and can hence be viewed as an entropically…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to an absolutely continuous curve on the $2$-Wasserstein…
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 the early 1930's, Erwin Schroedinger, motivated by his quest for a more classical formulation of quantum mechanics, posed a large deviation problem for a cloud of independent Brownian particles. He showed that the solution to the problem…
We analyze the one dimensional Cucker-Smale (in short CS) model with a weak singular communication weight $\psi(x) = |x|^{-\beta}$ with $\beta \in (0,1)$. We first establish a global-in-time existence of measure-valued solutions to the…