Related papers: Strong c-concavity and stability in optimal transp…
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling $\pi_{\varepsilon}$ has sparse support for small regularization parameter $\varepsilon$, in contrast to entropic…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
We consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in R in the case where the cost function is concave. The…
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth…
We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and…
The cost functions considered are $c(x,y)=h(x-y)$, where $h\in C^2(\mathbb{R}^n)$, homogeneous of degree $p\geq 2$, with a positive definite Hessian in the unit sphere. We study multivalued monotone maps with respect to that cost and…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for…
Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models…
Fix a pair of smooth source and target densities $\rho$ and $\rho^*$ of equal mass, supported on bounded domains $\Omega, \Omega^* \subset \mathbb{R}^n$. Also fix a cost function $c_0 \in C^{4,\alpha}(\overline{\Omega} \times…
This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter reflects…