Decision-Weighted Flow Matching for Contextual Stochastic Optimization
For practitioners of stochastic optimization, this work provides a principled method to align generative model training with downstream decision quality, reducing regret in decision-sensitive regions.
Decision-Weighted Flow Matching (DW-FM) addresses objective mismatch in conditional generative models for stochastic optimization by reweighting the flow matching objective with decision-sensitive endpoint information, achieving improved downstream regret on three CVaR-based benchmarks.
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.