8 papers · 1 filter
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…