# Regularized Optimal Transport is Ground Cost Adversarial

arXiv: https://arxiv.org/abs/2002.03967 · HTML: https://mlsanity.com/paper/2002.03967/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 17 of 17)

- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [Regularized Policies are Reward Robust](https://mlsanity.com/paper/2101.07012/) (2021)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Energy-guided Entropic Neural Optimal Transport](https://mlsanity.com/paper/2304.06094/) (2023)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Rethinking Optimal Transport in Offline Reinforcement Learning](https://mlsanity.com/paper/2410.14069/) (2024)
- [Manifold optimization for non-linear optimal transport problems](https://mlsanity.com/paper/2103.00902/) (2021)
- [Structured Transforms Across Spaces with Cost-Regularized Optimal Transport](https://mlsanity.com/paper/2311.05788/) (2023)
- [Discrete Probabilistic Inverse Optimal Transport](https://mlsanity.com/paper/2112.09754/) (2021)
- [Unsupervised Ground Metric Learning using Wasserstein Singular Vectors](https://mlsanity.com/paper/2102.06278/) (2021)
- [Algorithms for Weak Optimal Transport with an Application to Economics](https://mlsanity.com/paper/2205.09825/) (2022)
- [Differentiable Cost-Parameterized Monge Map Estimators](https://mlsanity.com/paper/2406.08399/) (2024)
- [SoftJAX & SoftTorch: Empowering Automatic Differentiation Libraries with Informative Gradients](https://mlsanity.com/paper/2603.08824/) (2026)
- [Fast unsupervised ground metric learning with tree-Wasserstein distance](https://mlsanity.com/paper/2411.07432/) (2024)
- [Fractional Correspondence Framework in Detection Transformer](https://mlsanity.com/paper/2503.04107/) (2025)
- [Connecting adversarial attacks and optimal transport for domain adaptation](https://mlsanity.com/paper/2205.15424/) (2022)

## Abstract (arXiv)

Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better differentiation using the Sinkhorn algorithm, as well as better sample complexity bounds than classic OT. In this work we depart from this practical perspective and propose a new interpretation of regularization as a robust mechanism, and show using Fenchel duality that any convex regularization of OT can be interpreted as ground cost adversarial. This incidentally gives access to a robust dissimilarity measure on the ground space, which can in turn be used in other applications. We propose algorithms to compute this robust cost, and illustrate the interest of this approach empirically.