# Learning to Match via Inverse Optimal Transport

arXiv: https://arxiv.org/abs/1802.03644 · HTML: https://mlsanity.com/paper/1802.03644/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2018.

## Built on by (most cited first, 23 of 23)

- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [Learning High Dimensional Wasserstein Geodesics](https://mlsanity.com/paper/2102.02992/) (2021)
- [Revisiting Deep Audio-Text Retrieval Through the Lens of Transportation](https://mlsanity.com/paper/2405.10084/) (2024)
- [Approximating 1-Wasserstein Distance with Trees](https://mlsanity.com/paper/2206.12116/) (2022)
- [Functional optimal transport: map estimation and domain adaptation for functional data](https://mlsanity.com/paper/2102.03895/) (2021)
- [Discrete Probabilistic Inverse Optimal Transport](https://mlsanity.com/paper/2112.09754/) (2021)
- [Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport](https://mlsanity.com/paper/2212.14527/) (2022)
- [OTMatch: Improving Semi-Supervised Learning with Optimal Transport](https://mlsanity.com/paper/2310.17455/) (2023)
- [Double-Bounded Optimal Transport for Advanced Clustering and Classification](https://mlsanity.com/paper/2401.11418/) (2024)
- [Computing Approximate Graph Edit Distance via Optimal Transport](https://mlsanity.com/paper/2412.18857/) (2024)
- [Your contrastive learning problem is secretly a distribution alignment problem](https://mlsanity.com/paper/2502.20141/) (2025)
- [Unsupervised Ground Metric Learning using Wasserstein Singular Vectors](https://mlsanity.com/paper/2102.06278/) (2021)
- [S-MolSearch: 3D Semi-supervised Contrastive Learning for Bioactive Molecule Search](https://mlsanity.com/paper/2409.07462/) (2024)
- [Cracking Instance Jigsaw Puzzles: An Alternative to Multiple Instance Learning for Whole Slide Image Analysis](https://mlsanity.com/paper/2507.08178/) (2025)
- [Differentiable Cost-Parameterized Monge Map Estimators](https://mlsanity.com/paper/2406.08399/) (2024)
- [Fast unsupervised ground metric learning with tree-Wasserstein distance](https://mlsanity.com/paper/2411.07432/) (2024)
- [Enhancing 3D Medical Image Understanding with Pretraining Aided by 2D Multimodal Large Language Models](https://mlsanity.com/paper/2509.09064/) (2025)
- [Bridging Vision and Language Concepts through Optimal Transport Semantic Flow](https://mlsanity.com/paper/2606.26891/) (2026)
- [Connecting adversarial attacks and optimal transport for domain adaptation](https://mlsanity.com/paper/2205.15424/) (2022)
- [Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization](https://mlsanity.com/paper/2410.02628/) (2024)
- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)
- [CloneOT: predicting clone-specific perturbation responses with lineage-supervised neural inverse optimal transport](https://mlsanity.com/paper/2610.16093/) (2026)

## Abstract (arXiv)

We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching contexts. We emphasize that the discrete optimal transport plays the role of a variational principle which gives rise to an optimization-based framework for modeling the observed empirical matching data. Our formulation leads to a non-convex optimization problem which can be solved efficiently by an alternating optimization method. A key novel aspect of our formulation is the incorporation of marginal relaxation via regularized Wasserstein distance, significantly improving the robustness of the method in the face of noisy or missing empirical matching data. Our model falls into the category of prescriptive models, which not only predict potential future matching, but is also able to explain what leads to empirical matching and quantifies the impact of changes in matching factors. The proposed approach has wide applicability including predicting matching in online dating, labor market, college application and crowdsourcing. We back up our claims with numerical experiments on both synthetic data and real world data sets.