# Variable Selection for Feature-Based Newsvendor

arXiv: https://arxiv.org/abs/2609.01544 · HTML: https://mlsanity.com/paper/2609.01544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Applying Deep Learning to the Newsvendor Problem](https://mlsanity.com/paper/1607.02177/) (2016)
- [Sparse Classification: a scalable discrete optimization perspective](https://mlsanity.com/paper/1710.01352/) (2017)
- [Rank-one Convexification for Sparse Regression](https://mlsanity.com/paper/1901.10334/) (2019)
- [Variable Selection for Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.07415/) (2023)
- [Assessing the Performance of Deep Learning Algorithms for Newsvendor Problem](https://mlsanity.com/paper/1706.02899/) (2017)
- [Beyond Symmetry: Best Submatrix Selection for the Sparse Truncated SVD](https://mlsanity.com/paper/2105.03179/) (2021)
- [Variable selection in convex quantile regression: L1-norm or L0-norm regularization?](https://mlsanity.com/paper/2107.03119/) (2021)

## Abstract (arXiv)

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 ℓ0-constrained empirical newsvendor problem with ℓ2-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.