Distributionally robust stochastic programs with side information based on trimmings

• 成果类型: Article
• 署名作者: Esteban-Perez, Adrian; Morales, Juan M.
• 署名单位: Universidad de Malaga
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01724-0
• 发表日期: 2022
• 页码: 1069-1105
• 关键词: convergence

摘要

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.