Related papers: A Fast and Accurate Splitting Method for Optimal T…
Efficient trajectory optimization is essential for avoiding collisions in unstructured environments, but it remains challenging to have both speed and quality in the solutions. One reason is that second-order optimality requires calculating…
This paper presents consideration of the Semi-Relaxed Sinkhorn (SR-Sinkhorn) algorithm for the semi-relaxed optimal transport (SROT) problem, which relaxes one marginal constraint of the standard OT problem. For evaluation of how the…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…
We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based…
Entropic optimal transport (EOT) via Sinkhorn iterations is widely used in modern machine learning, yet GPU solvers remain inefficient at scale. Tensorized implementations suffer quadratic HBM traffic from dense $n\times m$ interactions,…
Optimal transmission switching (OTS) determines which transmission lines to remove from service to minimize dispatch costs. Unlike topology design, it alters the operational status of operating lines. Sensitivity-based methods, as advanced…
In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
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…
Reliable traversable area segmentation in unstructured environments is critical for planning and decision-making in autonomous driving. However, existing data-driven approaches often suffer from degraded segmentation performance in…
Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…
In this paper, we consider Strassen's version of optimal transport (OT) problem, which concerns minimizing the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…