2020/09/30 by Adrián Esteban-Pérez, Juan M. Morales · 8 citations
Decision Sciences · Energy · Mathematics · #Computer science #Context (archaeology) #Econometrics #Energy, Environment, and Transportation Policies #Fuzzy Systems and Optimization #Joint probability distribution #Kernel (algebra) #Kernel regression #Mathematical optimization #Mathematics #Newsvendor model #Nonparametric statistics #Risk and Portfolio Optimization #Robust optimization #Statistics #Stochastic programming #Supply chain #math.OC #msc:90C15 #msc:90C47
paper · pdf · doi:10.1007/s10107-021-01724-0
published in Mathematical Programming 195(1-2), 1069-1105 (Springer Science+Business Media) · 24 figures, 76 pages
arxiv created 2021/09/20 · openalex publication_date 2021/11/22 · arxiv updated 2021/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Abstract We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsic error in the process of inferring conditional information from limited joint data. We show that our approach is computationally as tractable as the standard (without side information) Wasserstein-metric-based DRO and enjoys performance guarantees. Furthermore, our DRO framework can be conveniently used to address data-driven decision-making problems under contaminated samples. Finally, the theoretical results are illustrated using a single-item newsvendor problem and a portfolio allocation problem with side information.