Related papers: Sparsity of Quadratically Regularized Optimal Tran…
Consider two bounded domains $\Omega$ and $\Lambda$ in $\mathbb{R}^{2}$, and two sufficiently regular probability measures $\mu$ and $\nu$ supported on them. By Brenier's theorem, there exists a unique transportation map $T$ satisfying…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
We study the solution of a large-scale transportation problem with an additional constraint on the sparsity of inbound flows. Such problems arise in the management of inventory for online retailers that operate with many order fulfillment…
Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential scaling. From an optimization viewpoint, the dual QOT…
Stability of the value function and the set of minimizers w.r.t. the given data is a desirable feature of optimal transport problems. For the classical Kantorovich transport problem, stability is satisfied under mild assumptions and in…
We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsically ill-posed, exhibiting…
We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.
We provide a new proof of the known partial regularity result for the optimal transportation map (Brenier map) between two sets. Contrary to the existing regularity theory for the Monge-Amp{\`e}re equation, which is based on the maximum…
The standard quadratic optimization problem (StQP), i.e. the problem of minimizing a quadratic form $\bold x^TQ\bold x$ on the standard simplex $\{\bold x\ge\bold 0: \bold x^T\bold e=1\}$, is studied. The StQP arises in numerous…
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…
We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote…
We determine the optimal structure of couplings for the \emph{Martingale transport problem} between radially symmetric initial and terminal laws $\mu, \nu$ on $\R^d$ and show the uniqueness of optimizer. Here optimality means that such…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of…
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…
In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal-dual regularization, the authors propose to…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…