Entropic regularization is one of the most active research areas in modern optimal transport. In many ways, it is simply another example of a regularization technique for the optimal transport problem. Indeed, w
We investigate the convergence properties of a continuous-time optimization method, the Mean-Field Best Response flow, for solving convex-concave min-max games with entropy regularization. We introduce suitable Lyapunov functions to establish exponential convergence to the unique mixed Nash equilibrium. Ad...
MATHEMATICAL regularizationORTHOTROPIC platesThis article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of optimal transport (Q-OT) corresponds to a relaxed version of the ...
Optimal transportEntropic regularizationSchrödinger potentialsWe study the potential functions that determine the optimal density for \\(\\varepsilon \\)-entropically regularized optimal transport, the so-called Schrdinger potentials, and their convergence to the counterparts in classical optimal transport...
Optimal transportentropy regularizationcentral limit theorembootstrapsensitivity analysiscountable spacesREGULARIZED OPTIMAL TRANSPORTALGORITHMSINFERENCEMATRICESFor probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the...
optimal transportentropic regularizationSinkhorn divergenceWasserstein distanceThis paper is devoted to the stochastic approximation of entropically regularized-Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal ...
In the limit $\\varepsilono0$ of vanishing regularization, strong compactness holds in $L^{1}$ and cluster points are Kantorovich potentials. In particular, the Schr\"odinger potentials converge in $L^{1}$ to the Kantorovich potentials as soon as the latter are unique. These results are ...
optimal transportentropy regularizationKullback--LeiblerBregman projectionconvex optimizationWasserstein barycentergeodesic distancelow-rank approximationsThe optimal transportation theory was successfully applied to different tasks on geometric domains as images and triangle meshes. In these applications the transport ...
In this work, we derive novel statistical bounds for empirical plug-in estimators of the EOT cost and show that their statistical performance in the entropy regularization parameter $\\varepsilon$ and the sample size $n$ only depends on the simpler of the two probability measures. For instance...
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the minimum mutual information property, namely, the joint measures of two Gaussian measures on Hilbert space with ...