2024/12/29 by Linglingzhi Zhu, Yunqin Zhu, Zhu, Linglingzhi +3 · 4 citations
Computer Science · Decision Sciences · Mathematics · #Algorithm #Computer science #Fuzzy Systems and Optimization #Mathematical optimization #Mathematics #Optimization algorithm #Risk and Portfolio Optimization #Robust optimization #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.2412.20556
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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. Unlike traditional discrete DRO approaches, which often suffer from scalability issues, limited generalization, and costly worst-case inference, our framework exploits Brenier's theorem to characterize the least favorable distribution as the pushforward of a transport map from a continuous reference measure. This characterization motivates our study of the minimax problem in Wasserstein space. We propose an iterative algorithmic framework with multiple variants and establish global convergence guarantees under mild assumptions, deriving complexity bounds in terms of subgradient evaluations and inexact Jordan-Kinderlehrer-Otto updates. Numerical results with neural network-based transport maps demonstrate that the proposed method enables both stable training of robust classifiers and effective worst-case inference for classification tasks.