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.
arXiv:2608.22746v1 Announce Type: new Abstract: This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distribut...
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
arXiv:2605. 10792v2 Announce Type: replace-cross Abstract: We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches.
The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.
arXiv:2505. 22839v2 Announce Type: replace-cross Abstract: Recent studies suggest that diffusion models significantly improve the empirical adversarial robustness of deep neural network models.
The paper rigorously analyzes the statistical and learning-theoretic properties of adversarial training models for classification, focusing on empirical optimal partial transport. It establishes two central limit theorems—one centered at the expected empirical value and another at the population value with smoothing—by leveraging the uniqueness of optimal potentials across various optimal transport formulations and empirical process theory. In the binary setting, the authors prove uniqueness of the optimal potential via a connection to multi-marginal optimal transport, and as additional results they derive stability of the saddle point, sample complexity, and concentration bounds for generalization error.
arXiv:2603. 07313v4 Announce Type: replace-cross Abstract: Robustness under latent distribution shift remains challenging in partially observable reinforcement learning.
arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.
arXiv:2608.29247v1 Announce Type: new Abstract: Deep neural networks remain highly vulnerable to adversarial perturbations, and adversarial training (AT) has become a widely used approach for improvi...
arXiv:2410. 07719v4 Announce Type: replace Abstract: Despite being widely adopted as a canonical framework for learning robust models, adversarial training suffers from robust overfitting.
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:2606. 19652v1 Announce Type: new Abstract: In this work, we introduce a training procedure for shallow neural networks that promotes robustness against adversarial attacks.