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Bilevel optimization for feature selection in the data-driven newsvendor problem

Breno Serrano, Stefan Minner, Maximilian Schiffer and Thibaut Vidal

Article (2024)

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Abstract

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.

Uncontrolled Keywords

Bilevel optimization; Newsvendor; Mixed integer programming.

Subjects: 2950 Applied mathematics > 2950 Applied mathematics
Department: Department of Mathematics and Industrial Engineering
Funders: Deutsche Forschungsgemeinschaft
Grant number: AdONE, GRK2201/277991500
PolyPublie URL: https://publications.polymtl.ca/57338/
Journal Title: European Journal of Operational Research (vol. 315, no. 2)
Publisher: Elsevier BV
DOI: 10.1016/j.ejor.2024.01.025
Official URL: https://doi.org/10.1016/j.ejor.2024.01.025
Date Deposited: 25 Mar 2024 14:33
Last Modified: 06 Apr 2024 09:21
Cite in APA 7: Serrano, B., Minner, S., Schiffer, M., & Vidal, T. (2024). Bilevel optimization for feature selection in the data-driven newsvendor problem. European Journal of Operational Research, 315(2), 703-714. https://doi.org/10.1016/j.ejor.2024.01.025

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