# Holistic Robust Data-Driven Decisions

arXiv: https://arxiv.org/abs/2207.09560 · HTML: https://mlsanity.com/paper/2207.09560/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 63 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 22 of 22)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defenses](https://mlsanity.com/paper/2012.10544/) (2020)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [From Data to Decisions: Distributionally Robust Optimization is Optimal](https://mlsanity.com/paper/1704.04118/) (2017)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization](https://mlsanity.com/paper/1605.09349/) (2016)
- [Robust Sample Average Approximation](https://mlsanity.com/paper/1408.4445/) (2014)
- [Likelihood Robust Optimization for Data-driven Problems](https://mlsanity.com/paper/1307.6279/) (2013)
- [Distributionally Robust Local Non-parametric Conditional Estimation](https://mlsanity.com/paper/2010.05373/) (2020)
- [On the power of adaptivity in statistical adversaries](https://mlsanity.com/paper/2111.10352/) (2021)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Two-stage sample robust optimization](https://mlsanity.com/paper/1907.07142/) (2019)
- [Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with ∞-Wasserstein Distance](https://mlsanity.com/paper/1908.08454/) (2019)

## Built on by (most cited first, 18 of 18)

- [Outlier-Robust Wasserstein DRO](https://mlsanity.com/paper/2311.05573/) (2023)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations](https://mlsanity.com/paper/2502.14105/) (2025)
- [Certified Robust Neural Networks: Generalization and Corruption Resistance](https://mlsanity.com/paper/2303.02251/) (2023)
- [Towards Fairness-Aware Adversarial Learning](https://mlsanity.com/paper/2402.17729/) (2024)
- [Generalization Bound and New Algorithm for Clean-Label Backdoor Attack](https://mlsanity.com/paper/2406.00588/) (2024)
- [Smoothed f-Divergence Distributionally Robust Optimization](https://mlsanity.com/paper/2306.14041/) (2023)
- [Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implications](https://mlsanity.com/paper/2311.05054/) (2023)
- [Robust Distribution Learning with Local and Global Adversarial Corruptions](https://mlsanity.com/paper/2406.06509/) (2024)
- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [Ensemble Modeling for Time Series Forecasting: an Adaptive Robust Optimization Approach](https://mlsanity.com/paper/2304.04308/) (2023)
- [Responsible AI (RAI) Games and Ensembles](https://mlsanity.com/paper/2310.18832/) (2023)
- [From Distributional Robustness to Robust Statistics: A Confidence Sets Perspective](https://mlsanity.com/paper/2410.14008/) (2024)
- [Distributionally Robust Optimization with Adversarial Data Contamination](https://mlsanity.com/paper/2507.10718/) (2025)
- [Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Balls](https://mlsanity.com/paper/2407.13625/) (2024)
- [Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2503.04315/) (2025)
- [Adversarial Training for Deep Hedging in Nonstationary Markets](https://mlsanity.com/paper/2610.07162/) (2026)

## Abstract (arXiv)

The design of data-driven formulations for machine learning and decision-making with good out-of-sample performance is a key challenge. The observation that good in-sample performance does not guarantee good out-of-sample performance is generally known as overfitting. Practical overfitting can typically not be attributed to a single cause but is caused by several factors simultaneously. We consider here three overfitting sources: (i) statistical error as a result of working with finite sample data, (ii) data noise, which occurs when the data points are measured only with finite precision, and finally, (iii) data misspecification in which a small fraction of all data may be wholly corrupted. Although existing data-driven formulations may be robust against one of these three sources in isolation, they do not provide holistic protection against all overfitting sources simultaneously. We design a novel data-driven formulation that guarantees such holistic protection and is computationally viable. Our distributionally robust optimization formulation can be interpreted as a novel combination of a Kullback-Leibler and L'evy-Prokhorov robust optimization formulation. In the context of classification and regression problems, we show that several popular regularized and robust formulations naturally reduce to a particular case of our proposed novel formulation. Finally, we apply the proposed HR formulation to two real-life applications and study it alongside several benchmarks: (1) training neural networks on healthcare data, where we analyze various robustness and generalization properties in the presence of noise, labeling errors, and scarce data, (2) a portfolio selection problem with real stock data, and analyze the risk/return tradeoff under the natural severe distribution shift of the application.