用扩散模型构建鲁棒优化的分布不确定性集，提升模型泛化能力。
Distributionally Robust Optimization via Diffusion Ambiguity Modeling
- 基于扩散模型构造对抗性分布的不确定性集，保持与原始分布一致。
- 在机器学习预测任务中显著优于传统方法，尤其在分布外数据上表现更优。
- 算法可解且理论收敛，适合需要高鲁棒性的实际场景。
本文研究分布鲁棒优化（DRO），一种增强统计学习与优化鲁棒性和泛化能力的基础框架。有效的不确定性集需包含与名义分布一致但足够多样、能覆盖多种潜在情形的分布，同时保证求解可处理。为此，我们提出一种基于扩散模型的不确定性集设计，能够捕捉超出名义支持空间的各类对抗性分布，同时保持与名义分布的一致性。基于此不确定性建模，我们提出扩散型分布鲁棒优化（D-DRO），一个通过参数化扩散模型空间求解内部最大化问题的可计算算法。我们形式化地建立了D-DRO的平稳收敛性能，并在机器学习预测任务中实证验证了其在分布外（OOD）泛化上的优越表现。
原文摘要 · Abstract (English)
This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions that remain consistent with the nominal distribution while being diverse enough to account for a variety of potential scenarios. Moreover, it should lead to tractable DRO solutions. To this end, we propose a diffusion-based ambiguity set design that captures various adversarial distributions beyond the nominal support space while maintaining consistency with the nominal distribution. Building on this ambiguity modeling, we propose Diffusion-based DRO (D-DRO), a tractable DRO algorithm that solves the inner maximization over the parameterized diffusion model space. We formally establish the stationary convergence performance of D-DRO and empirically demonstrate its superior Out-of-Distribution (OOD) generalization performance in a ML prediction task.
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