# Wasserstein Robust Classification with Fairness Constraints

arXiv: https://arxiv.org/abs/2103.06828 · HTML: https://mlsanity.com/paper/2103.06828/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 84 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 30 of 31)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Adversarial Logit Pairing](https://mlsanity.com/paper/1803.06373/) (2018)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (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)
- [Counterfactual Fairness in Text Classification through Robustness](https://mlsanity.com/paper/1809.10610/) (2018)
- [Automated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination](https://mlsanity.com/paper/1408.6491/) (2014)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Robust Optimization for Fairness with Noisy Protected Groups](https://mlsanity.com/paper/2002.09343/) (2020)
- [Training individually fair ML models with Sensitive Subspace Robustness](https://mlsanity.com/paper/1907.00020/) (2019)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [A Distributionally Robust Approach to Fair Classification](https://mlsanity.com/paper/2007.09530/) (2020)
- [R'enyi Fair Inference](https://mlsanity.com/paper/1906.12005/) (2019)
- [Stable and Fair Classification](https://mlsanity.com/paper/1902.07823/) (2019)
- [A Statistical Test for Probabilistic Fairness](https://mlsanity.com/paper/2012.04800/) (2020)
- [Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator](https://mlsanity.com/paper/1805.07194/) (2018)
- [Distributionally Robust Local Non-parametric Conditional Estimation](https://mlsanity.com/paper/2010.05373/) (2020)
- [Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms](https://mlsanity.com/paper/2012.12356/) (2020)
- [Adversarial Classification via Distributional Robustness with Wasserstein Ambiguity](https://mlsanity.com/paper/2005.13815/) (2020)

## Built on by (most cited first, 10 of 10)

- [Re-weighting Based Group Fairness Regularization via Classwise Robust Optimization](https://mlsanity.com/paper/2303.00442/) (2023)
- [Consistent Range Approximation for Fair Predictive Modeling](https://mlsanity.com/paper/2212.10839/) (2022)
- [On the Fairness ROAD: Robust Optimization for Adversarial Debiasing](https://mlsanity.com/paper/2310.18413/) (2023)
- [Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samples](https://mlsanity.com/paper/2310.07535/) (2023)
- [Learning Fair Policies for Multi-stage Selection Problems from Observational Data](https://mlsanity.com/paper/2312.13173/) (2023)
- [A Distributionally Robust Optimisation Approach to Fair Credit Scoring](https://mlsanity.com/paper/2402.01811/) (2024)
- [Auditing and Enforcing Conditional Fairness via Optimal Transport](https://mlsanity.com/paper/2410.14029/) (2024)
- [Risk-averse Fair Multi-class Classification](https://mlsanity.com/paper/2509.05771/) (2025)
- [From Fragile to Certified: Wasserstein Audits of Group Fairness Under Distribution Shift](https://mlsanity.com/paper/2509.26241/) (2025)
- [Fairness in multi-class multi-group classification problems via contextial coherent risk measures](https://mlsanity.com/paper/2608.30223/) (2026)

## Abstract (arXiv)

We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-∞ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive a conservative reformulation for the worst-case equal opportunity unfairness measure. We establish that the model is equivalent to a mixed binary optimization problem, which can be solved by standard off-the-shelf solvers. To improve scalability, we further propose a convex, hinge-loss-based model for large problem instances whose reformulation does not incur any binary variables. Moreover, we also consider the distributionally robust learning problem with a generic ground transportation cost to hedge against the uncertainties in the label and sensitive attribute. Finally, we numerically demonstrate that our proposed approaches improve fairness with negligible loss of predictive accuracy.