发表机构
Beijing University of Posts and Telecommunications; Nankai University; University of the Chinese Academy of Sciences; Southwest University of Finance and Economics（北京邮电大学; 南开大学; 中国科学院大学; 西南财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出免导数扩散框架D$^3$Opt，通过一次学习机会可行结构并冻结为先验，结合退火粒子Feynman--Kac修正，实现固定机会约束下非凸非光滑目标的免重训优化。
AI 中文摘要
机会约束规划（CCPs）在不确定性下通过限制约束违反的概率来优化决策。尽管传统方法和基于学习的方法取得了进展，但在固定机会约束下优化非凸或非光滑目标以及适应不同目标仍然具有挑战性。在本文中，我们提出了一个免导数的基于扩散的框架，将约束建模与目标优化解耦，称为D$^3$Opt。我们通过仅在约束过滤的决策上训练一个风险条件扩散模型，并冻结它作为后续指定目标的可复用先验，从而独立于任何特定目标地学习一次机会可行结构。在推理时，我们提出了一种退火的、基于粒子的Feynman--Kac修正，沿着冻结的反向扩散过程，仅使用函数评估来优化后续指定的目标。这使得无需针对特定目标重新训练即可对非凸和非光滑目标进行免导数优化。我们证明了当冻结先验具有可行性属性时，该修正保持可行性，并推导出一个优化误差界，该界将学习先验覆盖、有限粒子近似和有限温度效应分开。在线性高斯CCP、目标迁移任务和机会约束经济调度上的实验表明，该方法在光滑和非光滑目标（包括非凸情况）上均能有效优化，并在固定机会约束下无需重新训练即可实现目标泛化。
英文摘要
Chance-constrained programs (CCPs) optimize decisions under uncertainty by limiting the probability of constraint violation. Despite advances in traditional and learning-based approaches, optimizing non-convex or non-smooth objectives and adapting to different objectives under fixed chance constraints remain challenging. In this paper, we propose a \textbf{D}erivative-free \textbf{D}iffusion-based framework that \textbf{D}isentangles constraint modeling from objective optimization, termed \textbf{D$^3$Opt}. We learn the chance-feasible structure once, independently of any particular objective, by training a risk-conditioned diffusion model solely on constraint-filtered decisions and freezing it as a reusable prior for post-specified objectives. At inference time, we propose an annealed, particle-based Feynman--Kac correction along the frozen reverse diffusion process to optimize post-specified objectives using only function evaluations. This enables derivative-free optimization of non-convex and non-smooth objectives without objective-specific retraining. We prove that the correction preserves feasibility when this property holds for the frozen prior, and derive an optimization-error bound separating learned-prior coverage, finite-particle approximation, and finite-temperature effects. Experiments on linear Gaussian CCPs, objective-transfer tasks, and chance-constrained economic dispatch demonstrate effective optimization across smooth and non-smooth objectives, including non-convex cases, and objective generalization under fixed chance constraints without retraining.
