Related papers: Entropic Optimal Transport Problem with Convex Fun…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schr\"odinger potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb{R}^ d$. Our results hold under mild assumptions on the marginal…
The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application…
In this paper, we discuss our approach and algorithmic framework for solving large-scale security constrained optimal power flow (SCOPF) problems. SCOPF is a mixed integer non-convex optimization problem that aims to obtain the minimum…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
Entropic optimal transport -- the optimal transport problem regularized by KL diver\-gence -- is highly successful in statistical applications. Thanks to the smoothness of the entropic coupling, its sample complexity avoids the curse of…
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.
The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial,…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
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…
Classical entropy regularization is poorly suited to continuous-time martingale transport, since relative entropy between diffusion laws typically forces their volatility characteristics to coincide. We introduce a specific-entropy…
The Sinkhorn--Knopp (SK) algorithm is a cornerstone method for matrix scaling and entropically regularized optimal transport (EOT). Despite its empirical efficiency, existing theoretical guarantees to achieve a target marginal accuracy…
In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
We address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this…
Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Computing an OT problem requires solution of linear programming…
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…