Sharp Asymptotics for Regularized Optimal Transport

2026/07/20 by Carlos Cardoso-Perelló, Alberto González-Sanz, Marcel Nutz
#math.AP #math.OC #math.PR

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Abstract

We study the small-regularization limit for L^p-regularized optimal transport with 1<p<∞ and for entropically regularized optimal transport (EOT). The exact first-order (respectively, second-order) asymptotics are determined explicitly under mild assumptions on the source and target measures. Our work generalizes the existing results for quadratic and entropic regularization, and connects them by a natural interpolation via p∈(1,2). We derive all these asymptotics in a unified manner by a novel approach that separates the local computation of the optimal profile from the global enforcement of the marginal constraints: convex duality leads to Gaussian profiles for entropy and Barenblatt profiles for L^p-regularization, while a quantization construction turns these local profiles into couplings.

Citations

• From the Schrödinger problem to the Monge–Kantorovich problem
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices

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