Distributionally robust stochastic programs with side information based on trimmings -- Extended version

TL;DR

This paper introduces a new distributionally robust optimization framework leveraging trimmings and partial mass transportation to improve decision-making with limited joint data, providing computational tractability and performance guarantees.

Contribution

It develops a novel DRO approach based on trimmings linked to mass transportation, addressing data contamination and enhancing local nonparametric methods with theoretical guarantees.

Findings

Framework is computationally as tractable as standard Wasserstein DRO.

Provides performance guarantees for the proposed method.

Applied to newsvendor and portfolio problems with positive results.

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 and naturally produces distributionally robust versions of some local nonparametric predictive methods, such as Nadaraya-Watson kernel regression and $K$-nearest neighbors, which are often used in the context of conditional stochastic optimization. Finally, the theoretical results are illustrated using a single-item newsvendor problem and a portfolio allocation problem with side information.