Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing

What the math gives to ML

The paper turns Sinkhorn distributional robustness into a learnable generative adversary rather than a large conic optimization problem. Its transferable asset is the combination of kernel-smoothed reference measures, conditional-KL ambiguity, and Brenier maps represented as gradients of convex potentials; this yields invertible, differentiable distribution shifts with an explicit geometric constraint. A practical neural-network adaptation is to train a convex-potential transport augmenter that generates worst-case class-conditional examples during classifier training, enforcing a Sinkhorn/KL-radius budget and testing robustness under controlled distribution shift.