Related papers: Applications of optimal transport methods in the l…
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 study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
We propose two deep neural network-based methods for solving semi-martingale optimal transport problems. The first method is based on a relaxation/penalization of the terminal constraint, and is solved using deep neural networks. The second…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
We present an overview of our recent work on implementable solutions to the Schroedinger bridge problem and their potential application to optimal transport and various generalizations.
Global infrastructure robustness and local transport efficiency are critical requirements for transportation networks. However, since passengers often travel greedily to maximize their own benefit and trigger traffic jams, overall…
Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economical and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer…
This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal…
This work establishes that an optimal transport~(OT) problem regularized by a given $f$-divergence admits the same solution as another OT problem regularized by a different $g$-divergence, under an appropriate transformation of the cost…
We study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…