Variable Selection for Feature-Based Newsvendor
2026-09-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors look at how to pick a small number of important features (variables) to decide how much inventory to keep when demand is uncertain, which is called the newsvendor problem. They show that this selection problem is hard to solve exactly, so they create both an exact math approach and faster approximate methods to handle it. They also prove mathematically that their method works well with limited data and generalizes to new situations. Testing on fake and real data proves their method cuts down on unnecessary features while keeping costs low compared to other approaches.
newsvendor problemfeature selectioncardinality constraintmixed-integer programmingregularizationrandomized roundingsupport recoveryout-of-sample riskhigh-dimensional datainventory optimization
Authors
Zhaoliang Yuan, Jie Wang
Abstract
Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features. We formulate the resulting $\ell_0$-constrained empirical newsvendor problem with $\ell_2$-regularization, establish its computational hardness, and develop a mixed-integer second-order cone programming reformulation that strengthens the standard Big-$M$ formulation. To enable scalability beyond exact optimization, we develop a randomized-rounding algorithm with a bi-criteria guarantee and a greedy heuristic. Statistically, we provide theoretical analysis of the resulting sparse policy estimator, including finite-sample estimation error, out-of-sample risk bounds, and support recovery guarantees. Extensive experiments on both synthetic and real data illustrate the computational and statistical trade-offs among various baselines. Our results demonstrate that the proposed variable selection framework achieves competitive out-of-sample operational costs while using substantially fewer covariates.