# Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing

arXiv: https://arxiv.org/abs/2608.22746 · HTML: https://mlsanity.com/paper/2608.22746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 25 of 25)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Robust Hypothesis Testing Using Wasserstein Uncertainty Sets](https://mlsanity.com/paper/1805.10611/) (2018)
- [Flow-based Distributionally Robust Optimization](https://mlsanity.com/paper/2310.19253/) (2023)
- [A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2202.04258/) (2022)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces](https://mlsanity.com/paper/2412.20556/) (2024)
- [Robust Hypothesis Testing with Wasserstein Uncertainty Sets](https://mlsanity.com/paper/2105.14348/) (2021)
- [Worst-case generation via minimax optimization in Wasserstein space](https://mlsanity.com/paper/2512.08176/) (2025)
- [Assured autonomy: How operations research powers and orchestrates generative AI systems](https://mlsanity.com/paper/2512.23978/) (2025)
- [Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2403.14822/) (2024)
- [Gradient Flow Sampler-based Distributionally Robust Optimization](https://mlsanity.com/paper/2510.25956/) (2025)
- [Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport](https://mlsanity.com/paper/2604.26942/) (2026)
- [Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2512.12550/) (2025)
- [Contextual Distributionally Robust Optimization with Causal and Continuous Structure](https://mlsanity.com/paper/2601.11016/) (2026)
- [Sinkhorn Ambiguity Sets for Distributionally Robust Control: Convexity, Weak Compactness, and Tractability](https://mlsanity.com/paper/2605.03845/) (2026)

## Abstract (arXiv)

This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distributions in Sinkhorn discrepancy-based ambiguity sets centered at the empirical distributions. Existing approaches solve this problem by solving large-scale conic programs, which are not scalable. To overcome this, we propose a generative framework that learns least-favorable distributions and supports efficient training and end-to-end sampling. For the Sinkhorn discrepancy-based ambiguity sets, we first derive an equivalent conditional-KL-divergence representation with respect to kernel-smoothed reference distributions. This property allows us to prove strong duality for both constrained and unconstrained minimax SDRHT formulations. Based on the closed-form optimal detector and Brenier's theorem, we reformulate the max-min dual formulation as a maximization problem over convex potentials whose gradients characterize invertible transport maps between kernel-smoothed distributions and their least-favorable counterparts. We efficiently approximate these potentials using Hyper Input Convex Neural Networks (HyCNNs) equipped with stochastic gradient estimators and prove the representation power of HyCNNs and the distributional universality of their induced transport maps. Numerical results show that the proposed method achieves superior accuracy and robustness across different sample sizes and dimensions, while avoiding the scalability limitations of classical SDRHT methods.