Variable Selection for Feature-Based Newsvendor

• URL: http://arxiv.org/abs/2609.01544v1
• Date: Tue, 01 Sep 2026 17:10:24 GMT
• Title: Variable Selection for Feature-Based Newsvendor
• Abstract summary: Feature-based newsvendor models balance holding and shortage costs under demand uncertainty.<n>High-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs.<n>This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features.
• Score: 1.9851118379257533
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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