D³Opt：一次学习可行性、优化所有目标的免导数扩散模型

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Abstract: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.

Subjects:	Machine Learning (cs.LG); Optimization and Control (math.OC)
Cite as:	arXiv:2610.03071 [cs.LG]
	(or arXiv:2610.03071v1 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2610.03071 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Ziwen Liu [view email]
[v1] Fri, 2 Oct 2026 09:56:03 UTC (61 KB)