Worst-case generation via minimax optimization in Wasserstein space

• URL: http://arxiv.org/abs/2512.08176v1
• Date: Tue, 09 Dec 2025 02:11:08 GMT
• Title: Worst-case generation via minimax optimization in Wasserstein space
• Authors: Xiuyuan Cheng, Yao Xie, Linglingzhi Zhu, Yunqin Zhu,
• Abstract summary: Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts.<n>We develop a generative modeling framework for worst-case generation for a pre-specified risk.
• Score: 19.645939141861543
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts, in applications ranging from machine learning models to power grids and medical prediction systems. We develop a generative modeling framework for worst-case generation for a pre-specified risk, based on min-max optimization over continuous probability distributions, namely the Wasserstein space. Unlike traditional discrete distributionally robust optimization approaches, which often suffer from scalability issues, limited generalization, and costly worst-case inference, our framework exploits the Brenier theorem to characterize the least favorable (worst-case) distribution as the pushforward of a transport map from a continuous reference measure, enabling a continuous and expressive notion of risk-induced generation beyond classical discrete DRO formulations. Based on the min-max formulation, we propose a Gradient Descent Ascent (GDA)-type scheme that updates the decision model and the transport map in a single loop, establishing global convergence guarantees under mild regularity assumptions and possibly without convexity-concavity. We also propose to parameterize the transport map using a neural network that can be trained simultaneously with the GDA iterations by matching the transported training samples, thereby achieving a simulation-free approach. The efficiency of the proposed method as a risk-induced worst-case generator is validated by numerical experiments on synthetic and image data.

Related papers

• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Distributionally Robust Optimization with Adversarial Data Contamination [49.89480853499918]
  We focus on optimizing Wasserstein-1 DRO objectives for generalized linear models with convex Lipschitz loss functions.<n>Our primary contribution lies in a novel modeling framework that integrates robustness against training data contamination with robustness against distributional shifts.<n>This work establishes the first rigorous guarantees, supported by efficient computation, for learning under the dual challenges of data contamination and distributional shifts.
  arXiv  Detail & Related papers  (2025-07-14T18:34:10Z)
• Statistical Analysis of Conditional Group Distributionally Robust Optimization with Cross-Entropy Loss [16.1456465253627]
  We study multi-source unsupervised domain adaptation, where labeled data are available from multiple source domains and only unlabeled data are observed from the target domain.<n>We propose a novel Group Distributionally Conditional Optimization framework that learns a classifier by minimizing the worst-case cross-entropy loss over the convex combinations of the conditional outcome distributions from sources domains.<n>We establish fast statistical convergence rates for the empirical CG-DRO estimator by constructing two surrogate minimax optimization problems that serve as theoretical bridges.
  arXiv  Detail & Related papers  (2025-07-14T04:21:23Z)
• Generative Latent Neural PDE Solver using Flow Matching [8.397730500554047]
  We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space.<n>Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries.<n> Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability.
  arXiv  Detail & Related papers  (2025-03-28T16:44:28Z)
• Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions [22.765095010254118]
  The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques.
  arXiv  Detail & Related papers  (2024-07-31T19:45:27Z)
• Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization [29.24821214671497]
  Training machine learning and statistical models often involve optimizing a data-driven risk criterion. We propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations.
  arXiv  Detail & Related papers  (2024-01-28T21:19:15Z)
• Flow-based Distributionally Robust Optimization [23.232731771848883]
  We present a framework, called $textttFlowDRO$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets. We aim to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from it. We demonstrate its usage in adversarial learning, distributionally robust hypothesis testing, and a new mechanism for data-driven distribution perturbation differential privacy.
  arXiv  Detail & Related papers  (2023-10-30T03:53:31Z)
• Distributionally Robust Models with Parametric Likelihood Ratios [123.05074253513935]
  Three simple ideas allow us to train models with DRO using a broader class of parametric likelihood ratios. We find that models trained with the resulting parametric adversaries are consistently more robust to subpopulation shifts when compared to other DRO approaches.
  arXiv  Detail & Related papers  (2022-04-13T12:43:12Z)
• Which Invariance Should We Transfer? A Causal Minimax Learning Approach [18.71316951734806]
  We present a comprehensive minimax analysis from a causal perspective. We propose an efficient algorithm to search for the subset with minimal worst-case risk. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.
  arXiv  Detail & Related papers  (2021-07-05T09:07:29Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)
• Identification of Probability weighted ARX models with arbitrary domains [75.91002178647165]
  PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX) The architecture is conceived following the Mixture of Expert concept, developed within the machine learning field.
  arXiv  Detail & Related papers  (2020-09-29T12:50:33Z)
• Improving Maximum Likelihood Training for Text Generation with Density Ratio Estimation [51.091890311312085]
  We propose a new training scheme for auto-regressive sequence generative models, which is effective and stable when operating at large sample space encountered in text generation. Our method stably outperforms Maximum Likelihood Estimation and other state-of-the-art sequence generative models in terms of both quality and diversity.
  arXiv  Detail & Related papers  (2020-07-12T15:31:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.