Residuals-based distributionally robust optimization with covariate information
This work addresses the problem of improving decision-making under uncertainty for practitioners by integrating machine learning predictions into robust optimization, especially when data is scarce.
This paper explores data-driven methods for integrating machine learning prediction models into distributionally robust optimization (DRO) when joint observations of uncertain parameters and covariates are limited. The authors investigate the asymptotic and finite sample properties of solutions using various ambiguity sets (Wasserstein, sample robust optimization, and phi-divergence) and validate their effectiveness in limited data regimes, even with misspecified prediction models.
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.