# Distributionally Robust Prescriptive Analytics with Wasserstein Distance

arXiv: https://arxiv.org/abs/2106.05724 · HTML: https://mlsanity.com/paper/2106.05724/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [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)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [From Data to Decisions: Distributionally Robust Optimization is Optimal](https://mlsanity.com/paper/1704.04118/) (2017)
- [Robust Sample Average Approximation](https://mlsanity.com/paper/1408.4445/) (2014)
- [Wasserstein Distributionally Robust Optimization and Variation Regularization](https://mlsanity.com/paper/1712.06050/) (2017)
- [Residuals-based distributionally robust optimization with covariate information](https://mlsanity.com/paper/2012.01088/) (2020)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [Distributionally Robust Local Non-parametric Conditional Estimation](https://mlsanity.com/paper/2010.05373/) (2020)
- [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)
- [Distributionally Robust Optimization with Correlated Data from Vector Autoregressive Processes](https://mlsanity.com/paper/1909.03433/) (2019)
- [Dimension Reduction in Contextual Online Learning via Nonparametric Variable Selection](https://mlsanity.com/paper/2009.08265/) (2020)
- [Distributionally Robust Parametric Maximum Likelihood Estimation](https://mlsanity.com/paper/2010.05321/) (2020)

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

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Robust personalized pricing under uncertainty of purchase probabilities](https://mlsanity.com/paper/2407.15332/) (2024)

## Abstract (arXiv)

In prescriptive analytics, the decision-maker observes historical samples of (X, Y), where Y is the uncertain problem parameter and X is the concurrent covariate, without knowing the joint distribution. Given an additional covariate observation x, the goal is to choose a decision z conditional on this observation to minimize the cost mathbbE[c(z,Y)|X=x]. This paper proposes a new distributionally robust approach under Wasserstein ambiguity sets, in which the nominal distribution of Y|X=x is constructed based on the Nadaraya-Watson kernel estimator concerning the historical data. We show that the nominal distribution converges to the actual conditional distribution under the Wasserstein distance. We establish the out-of-sample guarantees and the computational tractability of the framework. Through synthetic and empirical experiments about the newsvendor problem and portfolio optimization, we demonstrate the strong performance and practical value of the proposed framework.