Decision-Weighted Flow Matching for Contextual Stochastic Optimization
2026-06-15 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors identify that usual methods for training models to create scenarios in optimization focus on matching data patterns evenly, but this can lead to mistakes in important decision areas. They develop a new training method called Decision-Weighted Flow Matching (DW-FM) that emphasizes parts of the data affecting final decisions more heavily. Their theory links decision errors to mismatches in model behavior, and their approach adjusts training to reduce these errors. Tests on financial and traffic examples show that DW-FM helps make better decisions compared to traditional methods.
Conditional generative modelsStochastic optimizationDecision regretFlow matchingVelocity regressionCVaR (Conditional Value at Risk)Scenario generationRegret alignmentAdjoint transportDownstream decisions
Authors
Jize Xie, Haomiao Wu, Qiang Chen, Xiu Su, Yi Chen
Abstract
Conditional generative models are increasingly used as scenario generators for stochastic optimization, but standard training objectives emphasize uniform distributional fit rather than the downstream decisions induced by generated scenarios. This creates an objective mismatch: errors in statistically common regions may have little effect on decision regret, whereas errors in decision-sensitive regions can substantially change the optimal action. We propose Decision-Weighted Flow Matching (DW-FM), a regret-aligned training framework that preserves the simplicity of standard flow matching while reweighting its velocity-regression objective using decision-sensitive endpoint information. Theoretically, we connect downstream regret to pathwise velocity mismatch through a loss-induced decision discrepancy and an adjoint transport argument, yielding an ideal regret-aligned surrogate and practical endpoint-weighted objectives with regret guarantees. Empirically, we demonstrate the effectiveness of DW-FM on three CVaR-based contextual stochastic optimization benchmarks spanning synthetic portfolio, semi-real financial, and traffic-CVaR tasks, where DW-FM improves downstream regret over standard baselines.