![[2502.01310] A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2502.01310] A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers
Summary
This article presents a statistical learning perspective on semi-dual adversarial neural optimal transport solvers, addressing theoretical gaps in existing methods and establishing generalization error bounds.
Why It Matters
Understanding the theoretical foundations of neural optimal transport methods is crucial for advancing generative modeling applications in various fields. This work provides essential insights into the performance and reliability of these methods, which can influence future research and practical implementations.
Key Takeaways
- The paper establishes upper bounds on the generalization error for minimax quadratic optimal transport solvers.
- It highlights the lack of theoretical investigation in existing adversarial minimax solvers.
- The findings could pave the way for similar theoretical developments in general optimal transport cases.
- Applications of neural optimal transport span multiple fields, including image processing and computational biology.
- The research emphasizes the importance of statistical properties in evaluating neural network performance.
Computer Science > Machine Learning arXiv:2502.01310 (cs) [Submitted on 3 Feb 2025 (v1), last revised 24 Feb 2026 (this version, v4)] Title:A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers Authors:Roman Tarasov, Petr Mokrov, Milena Gazdieva, Evgeny Burnaev, Alexander Korotin View a PDF of the paper titled A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers, by Roman Tarasov and 4 other authors View PDF HTML (experimental) Abstract:Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experi...