Decision-Aware Generative Demand Learning for Contextual Newsvendor Optimization via Quantile Sensitivities

Contextual newsvendor optimization is important in operations management because context-dependent demand and cost asymmetry jointly determine inventory decisions. For one fixed shortage-to-overage cost ratio, the optimum is a single conditional quantile, so direct policy learning can suffice; a conditional demand distribution is instead valuable when costs or downstream uses change. We propose Regularized Smart Estimate-Then-Optimize (RSETO), which combines conditional likelihood with smoothed newsvendor loss. Building on existing quantile-sensitivity identities, a decision-weighted batched order-statistic infinitesimal perturbation analysis (IPA) estimator supplies vector-parameter gradients without evaluating a conditional CDF or density. We prove fixed-parameter mean-square consistency and, under an explicit trajectory-wise approximation condition and projected stochastic-approximation assumptions, almost-sure convergence to the constrained stationary set of the smoothed empirical objective. Experiments show that RSETO improves design-setting decision performance over likelihood-only training, especially at a extreme-tail target, while preserving the ability to adapt decisions across cost settings.