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We consider data-driven approaches that integrate a machine learningprediction model within distributionally robust optimization (DRO) givenlimited joint observations of uncertain parameters and covariates. Ourframework is flexible in the sense that it can accommodate a variety ofregression setups and DRO ambiguity sets. We investigate asymptotic and finitesample properties of solutions obtained using Wasserstein, sample robustoptimization, and phi-divergence-based ambiguity sets within our DROformulations, and explore cross-validation approaches for sizing theseambiguity sets. Through numerical experiments, we validate our theoreticalresults, study the effectiveness of our approaches for sizing ambiguity sets,and illustrate the benefits of our DRO formulations in the limited data regimeeven when the prediction model is misspecified.

Residuals-based distributionally robust optimization with covariate information