# Orlicz space regularization of continuous optimal transport problems

arXiv: https://arxiv.org/abs/2004.11574 · HTML: https://mlsanity.com/paper/2004.11574/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2020.

## Built on by (most cited first, 5 of 5)

- [Generalized Sobolev Transport for Probability Measures on a Graph](https://mlsanity.com/paper/2402.04516/) (2024)
- [Variational Online Mirror Descent for Robust Learning in Schr"odinger Bridge](https://mlsanity.com/paper/2504.02618/) (2025)
- [An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graph](https://mlsanity.com/paper/2502.00739/) (2025)
- [Generalized Sobolev IPM for Graph-Based Measures](https://mlsanity.com/paper/2510.25591/) (2025)
- [Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysis](https://mlsanity.com/paper/2605.24644/) (2026)

## Abstract (arXiv)

In this work we analyze regularized optimal transport problems in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, the aim is to find a transport plan, which is another Radon measure on the product of the sets, that has these two measures as marginals and minimizes the sum of a certain linear cost function and a regularization term. We focus on regularization terms where a Young's function applied to the (density of the) transport plan is integrated against a product measure. This forces the transport plan to belong to a certain Orlicz space. The predual problem is derived and proofs for strong duality and existence of primal solutions of the regularized problem are presented. Existence of (pre-)dual solutions is shown for the special case of Lp regularization for p≥ 2. Moreover, two results regarding Gamma-convergence are stated: The first is concerned with marginals that do not lie in the appropriate Orlicz space and guarantees Gamma-convergence to the original Kantorovich problem, when smoothing the marginals. The second results gives convergence of a regularized and discretized problem to the unregularized, continuous problem.