# Empirical Risk Minimization under Fairness Constraints

arXiv: https://arxiv.org/abs/1802.08626 · HTML: https://mlsanity.com/paper/1802.08626/

## Key facts

- Cited by 226 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2018.

## Built on by (most cited first, 30 of 226)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Label-Imbalanced and Group-Sensitive Classification under Overparameterization](https://mlsanity.com/paper/2103.01550/) (2021)
- [Mitigating Political Bias in Language Models Through Reinforced Calibration](https://mlsanity.com/paper/2104.14795/) (2021)
- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [Causally motivated Shortcut Removal Using Auxiliary Labels](https://mlsanity.com/paper/2105.06422/) (2021)
- [Leveling Down in Computer Vision: Pareto Inefficiencies in Fair Deep Classifiers](https://mlsanity.com/paper/2203.04913/) (2022)
- [AutoBalance: Optimized Loss Functions for Imbalanced Data](https://mlsanity.com/paper/2201.01212/) (2022)
- [FairLex: A Multilingual Benchmark for Evaluating Fairness in Legal Text Processing](https://mlsanity.com/paper/2203.07228/) (2022)
- [Improving Conditional Coverage via Orthogonal Quantile Regression](https://mlsanity.com/paper/2106.00394/) (2021)
- [Unsupervised Learning of Debiased Representations with Pseudo-Attributes](https://mlsanity.com/paper/2108.02943/) (2021)
- [On Tilted Losses in Machine Learning: Theory and Applications](https://mlsanity.com/paper/2109.06141/) (2021)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [Achieving Fairness at No Utility Cost via Data Reweighing with Influence](https://mlsanity.com/paper/2202.00787/) (2022)
- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [On Learning Fairness and Accuracy on Multiple Subgroups](https://mlsanity.com/paper/2210.10837/) (2022)
- [Simple and near-optimal algorithms for hidden stratification and multi-group learning](https://mlsanity.com/paper/2112.12181/) (2021)
- [A Stochastic Optimization Framework for Fair Risk Minimization](https://mlsanity.com/paper/2102.12586/) (2021)
- [Training Fair Models in Federated Learning without Data Privacy Infringement](https://mlsanity.com/paper/2109.05662/) (2021)
- [Rethinking Bias Mitigation: Fairer Architectures Make for Fairer Face Recognition](https://mlsanity.com/paper/2210.09943/) (2022)
- [Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values](https://mlsanity.com/paper/2109.10431/) (2021)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Assessing Fairness in the Presence of Missing Data](https://mlsanity.com/paper/2112.04899/) (2021)
- [Testing Group Fairness via Optimal Transport Projections](https://mlsanity.com/paper/2106.01070/) (2021)
- [Multi-objective Asynchronous Successive Halving](https://mlsanity.com/paper/2106.12639/) (2021)
- [Marrying Fairness and Explainability in Supervised Learning](https://mlsanity.com/paper/2204.02947/) (2022)
- [FairTune: Optimizing Parameter Efficient Fine Tuning for Fairness in Medical Image Analysis](https://mlsanity.com/paper/2310.05055/) (2023)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Optimising Equal Opportunity Fairness in Model Training](https://mlsanity.com/paper/2205.02393/) (2022)
- [Transferring Fairness under Distribution Shifts via Fair Consistency Regularization](https://mlsanity.com/paper/2206.12796/) (2022)
- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)

## Abstract (arXiv)

We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our approach. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches.