Gradient Flow Sampler-based Distributionally Robust Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910255936438272 |
|---|---|
| author | Xu, Zusen Zhu, Jia-Jie |
| author_facet | Xu, Zusen Zhu, Jia-Jie |
| contents | We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show that our theoretical framework can be implemented as practical algorithms for sampling from worst-case distributions and, consequently, DRO. While numerous previous works have proposed various reformulation techniques and iterative algorithms, we contribute a sound gradient flow view of the distributional optimization that can be used to construct new algorithms. As an example of applications, we solve a class of Wasserstein and Sinkhorn DRO problems using the recently-discovered Wasserstein Fisher-Rao and Stein variational gradient flows. Notably, we also show some simple reductions of our framework recover exactly previously proposed popular DRO methods, and provide new insights into their theoretical limit and optimization dynamics. Numerical studies based on stochastic gradient descent provide empirical backing for our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient Flow Sampler-based Distributionally Robust Optimization Xu, Zusen Zhu, Jia-Jie Optimization and Control Analysis of PDEs Machine Learning We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show that our theoretical framework can be implemented as practical algorithms for sampling from worst-case distributions and, consequently, DRO. While numerous previous works have proposed various reformulation techniques and iterative algorithms, we contribute a sound gradient flow view of the distributional optimization that can be used to construct new algorithms. As an example of applications, we solve a class of Wasserstein and Sinkhorn DRO problems using the recently-discovered Wasserstein Fisher-Rao and Stein variational gradient flows. Notably, we also show some simple reductions of our framework recover exactly previously proposed popular DRO methods, and provide new insights into their theoretical limit and optimization dynamics. Numerical studies based on stochastic gradient descent provide empirical backing for our theoretical findings. |
| title | Gradient Flow Sampler-based Distributionally Robust Optimization |
| topic | Optimization and Control Analysis of PDEs Machine Learning |
| url | https://arxiv.org/abs/2510.25956 |