16 papers
Geometry and Convergence of Quadratically Regularized Optimal Transport II
Alberto González-Sanz, Marcel Nutz
We study quadratically regularized optimal transport with quadratic cost in the regime of small regularization , where the support of the optimal coupling is sparse. F…
Geometry and Convergence of Quadratically Regularized Optimal Transport I
Alberto González-Sanz, Marcel Nutz
We establish sharp convergence rates for quadratically regularized optimal transport with quadratic cost in the regime of small regularization . In particular, we quan…
Sharp Asymptotics for Regularized Optimal Transport
Carlos Cardoso-Perelló, Alberto González-Sanz, Marcel Nutz
We study the small-regularization limit for -regularized optimal transport with and for entropically regularized optimal transport (EOT). The exact first-order (r…
Finite-sample bounds for regularized optimal transport
Alberto González-Sanz, Marcel Nutz, Austin J. Stromme
We study the sample complexity of regularized optimal transport for general convex regularizations including the Kullback--Leibler divergence and penalties. Our main results…
Stability of Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz
Quadratically regularized optimal transport (QOT) is a sparse alternative to entropic optimal transport. We develop a quantitative stability theory for QOT under perturbations of t…
Polyak-Lojasiewicz Inequality for Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential sc…
Entropic regularization of Monge's problem
Marcel Nutz, Chenyang Zhong
We study the vanishing-regularization limit of entropically regularized optimal transport (EOT) for the Euclidean distance cost in dimension . We develop a co…
Bid--Ask Martingale Optimal Transport
Bryan Liang, Marcel Nutz, Shunan Sheng +1
Martingale Optimal Transport (MOT) provides a framework for robust pricing and hedging of illiquid derivatives. Classical MOT enforces exact calibration of model marginals to the m…
Sample Complexity of Quadratically Regularized Optimal Transport
Alberto González-Sanz, Eustasio del Barrio, Marcel Nutz
It is well known that optimal transport suffers from the curse of dimensionality: when the prescribed marginals are approximated by i.i.d. samples, the convergence of the empirical…
Linear Convergence of Gradient Descent for Quadratically Regularized Optimal Transport
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regulari…
Stability of Mean-Field Variational Inference
Shunan Sheng, Bohan Wu, Alberto González-Sanz +1
Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. This paper studies the stability p…
Sparse Regularized Optimal Transport without Curse of Dimensionality
Alberto González-Sanz, Stephan Eckstein, Marcel Nutz
Entropic optimal transport -- the optimal transport problem regularized by KL diver\-gence -- is highly successful in statistical applications. Thanks to the smoothness of the entr…
Sparsity of Quadratically Regularized Optimal Transport: Scalar Case
Alberto González-Sanz, Marcel Nutz
The quadratically regularized optimal transport problem is empirically known to have sparse solutions: its optimal coupling has sparse support for small regulariz…
Monotonicity in Quadratically Regularized Linear Programs
Alberto González-Sanz, Marcel Nutz, Andrés Riveros Valdevenito
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience sugges…
Quantitative Convergence of Quadratically Regularized Linear Programs
Alberto González-Sanz, Marcel Nutz
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penal…
Quadratically Regularized Optimal Transport: Existence and Multiplicity of Potentials
Marcel Nutz
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called po…