提出新算法解决连续分布鲁棒优化难题，提升模型抗干扰能力。
Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces
- 利用Brenier定理将最坏分布建模为参考分布的映射结果
- 算法在Wasserstein空间实现全局收敛，复杂度可控
- 适用于需稳定训练和可靠推理的分类任务
我们研究连续概率空间下的分布鲁棒优化（DRO），以实现稳健推断。由于最坏情况分布为连续分布，导致优化问题具有无限维特性，带来显著计算挑战。与传统离散DRO方法相比，该方法利用Brenier定理，将最不利分布刻画为从连续参考测度出发的传输映射的像，从而推动在Wasserstein空间中对极小极大问题的研究。本文提出一种迭代算法框架，包含多种变体，并在弱假设下建立了全局收敛性保证，导出了基于次梯度评估次数和不精确Jordan-Kinderlehrer-Otto更新的复杂度界。基于神经网络的传输映射的数值实验表明，所提方法能实现鲁棒分类器的稳定训练，并有效支持分类任务中的最坏情况推断。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。