Generative Decision-Focused Learning for Multistage Stochastic Convex Programming

We propose generative decision-focused learning (DFL) for multistage stochastic convex programs implemented through rolling two-stage approximation. The autoregressive conditional diffusion model generates scenarios from the distribution of uncertainty given the observed history, and its parameters are updated using the realized cost of the decisions returned by the downstream stochastic program rather than prediction loss. To propagate the decision loss through the optimization layer, the sensitivity of the optimal solution to the learned uncertainty distribution is characterized by differentiating the Karush-Kuhn-Tucker (KKT) system. We consider three gradient estimators that differ in their treatment of scenario-dependent constraints and distributional derivatives: expected-constraint reparameterization, scenario-wise reparameterization, and an expected-constraint score-function surrogate. Across the inventory control, power dispatch, and bike-rebalancing applications, expected-constraint reparameterization outperforms predict-then-optimize at all scenario sample sizes considered.