# From Data to Decisions: Distributionally Robust Optimization is Optimal

arXiv: https://arxiv.org/abs/1704.04118 · HTML: https://mlsanity.com/paper/1704.04118/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2017.

## Built on by (most cited first, 30 of 38)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [On the Optimality of Batch Policy Optimization Algorithms](https://mlsanity.com/paper/2104.02293/) (2021)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Holistic Robust Data-Driven Decisions](https://mlsanity.com/paper/2207.09560/) (2022)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Certified Robust Neural Networks: Generalization and Corruption Resistance](https://mlsanity.com/paper/2303.02251/) (2023)
- [Group Distributionally Robust Dataset Distillation with Risk Minimization](https://mlsanity.com/paper/2402.04676/) (2024)
- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Smoothed f-Divergence Distributionally Robust Optimization](https://mlsanity.com/paper/2306.14041/) (2023)
- [Robust Generalization despite Distribution Shift via Minimum Discriminating Information](https://mlsanity.com/paper/2106.04443/) (2021)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Distributionally Robust Optimization with Markovian Data](https://mlsanity.com/paper/2106.06741/) (2021)
- [Explainability's Gain is Optimality's Loss? -- How Explanations Bias Decision-making](https://mlsanity.com/paper/2206.08705/) (2022)
- [Minimax Optimal Estimation of Stability Under Distribution Shift](https://mlsanity.com/paper/2212.06338/) (2022)
- [Human Imperceptible Attacks and Applications to Improve Fairness](https://mlsanity.com/paper/2111.15603/) (2021)
- [Online Decision Making for Trading Wind Energy](https://mlsanity.com/paper/2209.02009/) (2022)
- [Distributional Robustness Bounds Generalization Errors](https://mlsanity.com/paper/2212.09962/) (2022)
- [Towards Optimal Offline Reinforcement Learning](https://mlsanity.com/paper/2503.12283/) (2025)
- [Decision Making Needs Uncertainty Quantification [Lecture Notes]](https://mlsanity.com/paper/2607.14407/) (2026)
- [Efficient Data-Driven Optimization with Noisy Data](https://mlsanity.com/paper/2102.04363/) (2021)
- [Robust Phi-Divergence MDPs](https://mlsanity.com/paper/2205.14202/) (2022)
- [Optimal Confidence Intervals via Moderate Deviations Theory](https://mlsanity.com/paper/2305.14496/) (2023)
- [From Distributional Robustness to Robust Statistics: A Confidence Sets Perspective](https://mlsanity.com/paper/2410.14008/) (2024)
- [On a class of data-driven mixed-integer programming problems under uncertainty: a distributionally robust approach](https://mlsanity.com/paper/2105.14139/) (2021)
- [Distributionally Robust Optimization using Cost-Aware Ambiguity Sets](https://mlsanity.com/paper/2303.09408/) (2023)
- [Robust Data-driven Prescriptiveness Optimization](https://mlsanity.com/paper/2306.05937/) (2023)

## Abstract (arXiv)

We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transforms the data to an estimate of the expected cost function under the unknown data-generating distribution, i.e., a predictor, and an optimizer of the estimated cost function that serves as a near-optimal candidate decision, i.e., a prescriptor. As functions of the data, predictors and prescriptors constitute statistical estimators. We propose a meta-optimization problem to find the least conservative predictors and prescriptors subject to constraints on their out-of-sample disappointment. The out-of-sample disappointment quantifies the probability that the actual expected cost of the candidate decision under the unknown true distribution exceeds its predicted cost. Leveraging tools from large deviations theory, we prove that this meta-optimization problem admits a unique solution: The best predictor-prescriptor pair is obtained by solving a distributionally robust optimization problem over all distributions within a given relative entropy distance from the empirical distribution of the data.