# Bilevel Optimization for Feature Selection in the Data-Driven Newsvendor Problem

arXiv: https://arxiv.org/abs/2209.05093 · HTML: https://mlsanity.com/paper/2209.05093/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 13 of 13)

- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions](https://mlsanity.com/paper/1903.03088/) (2019)
- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Robust Sample Average Approximation](https://mlsanity.com/paper/1408.4445/) (2014)
- [Applying Deep Learning to the Newsvendor Problem](https://mlsanity.com/paper/1607.02177/) (2016)
- [Likelihood Robust Optimization for Data-driven Problems](https://mlsanity.com/paper/1307.6279/) (2013)
- [How Big Should Your Data Really Be? Data-Driven Newsvendor: Learning One Sample at a Time](https://mlsanity.com/paper/2107.02742/) (2021)
- [Assessing the Performance of Deep Learning Algorithms for Newsvendor Problem](https://mlsanity.com/paper/1706.02899/) (2017)
- [Subset Selection for Multiple Linear Regression via Optimization](https://mlsanity.com/paper/1701.07920/) (2017)
- [Minimization of Akaike's Information Criterion in Linear Regression Analysis via Mixed Integer Nonlinear Program](https://mlsanity.com/paper/1606.05030/) (2016)

## Built on by (most cited first, 3 of 3)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Contextual Stochastic Vehicle Routing with Time Windows](https://mlsanity.com/paper/2402.06968/) (2024)
- [OTPTO: Joint Product Selection and Inventory Optimization in Fresh E-commerce Front-End Warehouses](https://mlsanity.com/paper/2505.23421/) (2025)

## Abstract (arXiv)

We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse, explainable models with improved out-of-sample performance. Up to now, state-of-the-art methods utilize regularization, which penalizes the number of selected features or the norm of the solution vector. As an alternative, we introduce a novel bilevel programming formulation. The upper-level problem selects a subset of features that minimizes an estimate of the out-of-sample cost of ordering decisions based on a held-out validation set. The lower-level problem learns the optimal coefficients of the decision function on a training set, using only the features selected by the upper-level. We present a mixed integer linear program reformulation for the bilevel program, which can be solved to optimality with standard optimization solvers. Our computational experiments show that the method accurately recovers ground-truth features already for instances with a sample size of a few hundred observations. In contrast, regularization-based techniques often fail at feature recovery or require thousands of observations to obtain similar accuracy. Regarding out-of-sample generalization, we achieve improved or comparable cost performance.