Learn Feasibility Once, Optimize All Objectives: Derivative-Free Diffusion Models for Chance-Constrained Programming

2026-10-02

AI Summary

This study addresses the challenges of non-convex objective optimization and the high adaptation costs associated with multiple objectives in chance-constrained programming by proposing the D3Opt framework. This method decouples constraints from objectives through a risk-conditioned diffusion model combined with a particle Feynman–Kac correction, while freezing the diffusion prior to enable derivative-free optimization. The core contribution lies in achieving, for the first time, a “learn feasibility once, reuse across multiple objectives” paradigm that eliminates the need for retraining when encountering new objectives. Experimental results demonstrate that D3Opt efficiently handles both smooth and non-smooth objectives, exhibiting superior objective generalization capability and optimization efficiency under fixed constraints.

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.

Problem

• Chance-constrained programming
• Non-convex optimization
• Non-smooth objectives
• Derivative-free optimization
• Uncertainty

Innovation

• Chance-Constrained Programming
• Diffusion Models
• Derivative-Free Optimization
• Feynman-Kac Correction
• Constraint-Objective Disentanglement