arXiv AI

Generative Distributionally Robust Optimization

arXiv:2607. 24983v1 Announce Type: cross Abstract: Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data.

arXiv Statistics ML
Sep 28

Brenier Meets Adversarial Training: Optimal Transport Geometry for Robust Learning

The paper introduces a penalized distributionally robust optimization framework that allows an adversary to choose any distribution while incurring a Wasserstein penalty for deviating from the empirical distribution. It shows that the adversary’s problem can be reformulated as optimizing transport maps that push empirical samples to adversarial ones, proving that optimal maps are cyclically monotone. The authors argue that standard per-sample adversarial training violates this property and propose two remedies—multi-start particle ascent and input-convex neural network parameterization—to enforce cyclical monotonicity, demonstrating improved robustness and generalization in experiments on regression, image classification, and control tasks.

By Alireza Abdollahpoorrostam, Ehsan Sharifian, Buse \c{S}en, Marco Cuturi, Daniel Kuhn
arXiv Machine Learning
Jun 18

Generative models for decision-making under distributional shift

arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.

By Xiuyuan Cheng, Yunqin Zhu, Yao Xie