# Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls

arXiv: https://arxiv.org/abs/2406.02426 · HTML: https://mlsanity.com/paper/2406.02426/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Distributionally Robust Losses for Latent Covariate Mixtures](https://mlsanity.com/paper/2007.13982/) (2020)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Risk Guarantees for End-to-End Prediction and Optimization Processes](https://mlsanity.com/paper/2012.15046/) (2020)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)
- [Data-Pooling in Stochastic Optimization](https://mlsanity.com/paper/1906.00255/) (2019)
- [Dynamic optimization with side information](https://mlsanity.com/paper/1907.07307/) (2019)
- [Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts](https://mlsanity.com/paper/2106.00322/) (2021)
- [Bootstrap Robust Prescriptive Analytics](https://mlsanity.com/paper/1711.09974/) (2017)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach](https://mlsanity.com/paper/2110.04855/) (2021)
- [Beyond IID: data-driven decision-making in heterogeneous environments](https://mlsanity.com/paper/2206.09642/) (2022)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Distributionally Robust Data Join](https://mlsanity.com/paper/2202.05797/) (2022)
- [Distributionally Robust Optimal Power Flow with Contextual Information](https://mlsanity.com/paper/2109.07896/) (2021)

## Built on by (most cited first, 4 of 4)

- [Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Balls](https://mlsanity.com/paper/2407.13625/) (2024)
- [Robust Out-of-Distribution Stochastic Optimization](https://mlsanity.com/paper/2604.20147/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)
- [Domain Adaptation with Target Information via Doubly-Anchored Distributionally Robust Optimization](https://mlsanity.com/paper/2609.32730/) (2026)

## Abstract (arXiv)

In contextual optimization, a decision-maker leverages contextual information, often referred to as covariates, to better resolve uncertainty and make informed decisions. In this paper, we examine the challenges of contextual decision-making under covariate shift, a phenomenon where the distribution of covariates differs between the training and test environments. Such shifts can lead to inaccurate upstream estimations for test covariates that lie far from the training data, ultimately resulting in suboptimal downstream decisions. To tackle these challenges, we propose a novel approach called Intersection Wasserstein-balls DRO (IW-DRO), which integrates multiple estimation methods into the distributionally robust optimization (DRO) framework. At the core of our approach is an innovative ambiguity set defined as the intersection of two Wasserstein balls, with their centers constructed using appropriate nonparametric and parametric estimators. On the computational side, we reformulate the IW-DRO problem as a tractable convex program and develop an approximate algorithm tailored for large-scale problems to enhance computational efficiency. From a theoretical perspective, we demonstrate that IW-DRO achieves superior performance compared to single Wasserstein-ball DRO models. We further establish performance guarantees by analyzing the coverage of the intersection ambiguity set and the measure concentration of both estimators under the Wasserstein distance. Notably, we derive a finite-sample concentration result for the Nadaraya-Watson kernel estimator under covariate shift. The proposed IW-DRO framework offers practical value for decision-makers operating in uncertain environments affected by covariate shifts.