用扩散模型解决不确定优化问题，提升解的质量与稳定性。
A Gradient Guided Diffusion Framework for Chance Constrained Programming
- 基于梯度引导的扩散过程，仅需样本即可处理未知分布的不确定性。
- 通过噪声注入凸化可行域，实现渐近最优解生成，误差有理论保证。
- 在无线波形设计任务中性能优于现有方法，计算开销降低近80%。
机会约束规划（CCP）是应对不确定环境下优化问题的强大框架。本文提出一种新型梯度引导扩散优化框架GGDOpt，通过三项关键创新解决CCP问题：首先，无需知道不确定性的确切分布，仅依赖一组样本即可处理广泛类别的CCP问题；其次，为应对机会约束的非凸性，将CCP重构成在两个分布乘积上的采样问题——一个定义在非凸可行集上的未知数据分布，以及由目标函数决定的玻尔兹曼分布，从而充分利用一阶与二阶梯度信息；第三，GGDOpt在弱假设下具备理论收敛性并提供实用误差界。通过前向扩散过程中逐步注入噪声以凸化非凸可行区域，实现引导式反向采样，生成渐近最优解。在合成数据集和无线通信中的波形设计任务上的实验表明，相较于现有方法，GGDOpt在解质量与稳定性上均更优，且计算开销降低近80%。
原文摘要 · Abstract (English)
Chance constrained programming (CCP) is a powerful framework for addressing optimization problems under uncertainty. In this paper, we introduce a novel Gradient-Guided Diffusion-based Optimization framework, termed GGDOpt, which tackles CCP through three key innovations. First, GGDOpt accommodates a broad class of CCP problems without requiring the knowledge of the exact distribution of uncertainty-relying solely on a set of samples. Second, to address the nonconvexity of the chance constraints, it reformulates the CCP as a sampling problem over the product of two distributions: an unknown data distribution supported on a nonconvex set and a Boltzmann distribution defined by the objective function, which fully leverages both first- and second-order gradient information. Third, GGDOpt has theoretical convergence guarantees and provides practical error bounds under mild assumptions. By progressively injecting noise during the forward diffusion process to convexify the nonconvex feasible region, GGDOpt enables guided reverse sampling to generate asymptotically optimal solutions. Experimental results on synthetic datasets and a waveform design task in wireless communications demonstrate that GGDOpt outperforms existing methods in both solution quality and stability with nearly 80% overhead reduction.
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