# Residuals-based distributionally robust optimization with covariate information

arXiv: https://arxiv.org/abs/2012.01088 · HTML: https://mlsanity.com/paper/2012.01088/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2020.

## Built on by (most cited first, 21 of 21)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
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- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [Heteroscedasticity-aware residuals-based contextual stochastic optimization](https://mlsanity.com/paper/2101.03139/) (2021)
- [Adversarial Regression with Doubly Non-negative Weighting Matrices](https://mlsanity.com/paper/2109.14875/) (2021)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [End-to-End Fairness Optimization with Fair Decision-Focused Learning](https://mlsanity.com/paper/2607.29441/) (2026)
- [Robust Data-driven Prescriptiveness Optimization](https://mlsanity.com/paper/2306.05937/) (2023)
- [Prescribe-then-Select: Adaptive Policy Selection for Contextual Stochastic Optimization](https://mlsanity.com/paper/2509.08194/) (2025)
- [Distributionally Robust Recovery of Omitted Factors from Forecast Residuals with Application to Interest Rate Risk Management](https://mlsanity.com/paper/2601.04608/) (2026)
- [Autocorrelated Optimize-via-Estimate: Predict-then-Optimize versus Finite-sample Optimal](https://mlsanity.com/paper/2602.01877/) (2026)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)
- [Smooth Learning with Hard Constraints via Legendre-Regularized Policies](https://mlsanity.com/paper/2607.24007/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)
- [Largest Rashomon sets of decision trees for robust contextual optimization](https://mlsanity.com/paper/2610.04385/) (2026)

## Abstract (arXiv)

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.