A Sharp Comparison of Prescriptive Analytic Frameworks for The Big Data Newsvendor Problem

We study the feature-based newsvendor problem in high dimensions and provide sharp regret characterizations for three widely used prescriptive analytics approaches: the conventional Estimate-Then-Optimize (ETO), and the more recent end-to-end methods of Integrated-Learning-Optimization (ILO) & Direct Policy Optimization (DPO). Under well-specified linear demand model, we derive the regret results using convex Gaussian minmax theorem. Numerical explorations enabled by the results offer robust evidence of the superiority of ETO persisting even in high-dimensional regimes. Further, we highlight substantial performance gains attainable over all 3 methods by utilizing downstream optimization only in the model selection stage, instead of integrating it directly in training.