相关论文: A construction of the left-curtain coupling

Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity…

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…

A fluctuation theorem relating the work to its optimal average work is presented. The function mediating the relation is increasing and convex, and depends on the switching time $\tau$, driving strength $\delta\lambda/\lambda_0$, and…

We study the Monge--Kantorovich problem with one-dimensional marginals $\mu$ and $\nu$ and the cost function $c = \min\{l_1, \ldots, l_n\}$ that equals the minimum of a finite number $n$ of affine functions $l_i$ satisfying certain…

A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential…

During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…

We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension…

We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…

In this paper we consider the Benamou-Brenier formulation of optimal transport for nonlinear control affine systems on $\Rd$, removing the compactness assumption of the underlying manifold in previous work by the author. By using Bernard's…

Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…

We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous optimal transport (SOT). The new framework is motivated by the need to transport resources of different types simultaneously,…

In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures. We formulate the above as a generalized optimal transport problem where the cost, the marginals, and the coupling…

We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight…

The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschitz functions. This result has been widely used in various…

The optimal transportation problem, first suggested by Gaspard Monge in the 18th century and later revived in the 1940s by Leonid Kantorovich, deals with the question of transporting a certain measure to another, using transport maps or…

For a family of probability spaces $\{(X_k,\mathcal{B}_{X_k},\mu_k)\}_{k=1}^N$ and a cost function $c: X_1\times\cdots\times X_N\to \mathbb{R}$ we consider the Monge-Kantorovich problem \begin{align*}\tag{MK}\label{MONKANT}…

We study the optimal routing problem in decentralized exchanges built on Constant Function Market Makers when trades can be split across multiple heterogeneous pools and execution incurs fixed on-chain costs (gas fees). While prior routing…

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…

For probability measures $\mu,\nu$ and $\rho$ define the cost functionals \begin{align*} C(\mu,\rho):=\sup_{\pi\in \Pi(\mu,\rho)} \int \langle x,y\rangle\, \pi(dx,dy),\quad C(\nu,\rho):=\sup_{\pi\in \Pi(\nu,\rho)} \int \langle x,y\rangle\,…