# Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing

arXiv: https://arxiv.org/abs/2104.01634 · HTML: https://mlsanity.com/paper/2104.01634/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 71 references that are in the map.
- First posted on arXiv 4 Apr 2021.

## Builds on (most cited first, 30 of 34)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Minimax Pareto Fairness: A Multi Objective Perspective](https://mlsanity.com/paper/2011.01821/) (2020)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [From Parity to Preference-based Notions of Fairness in Classification](https://mlsanity.com/paper/1707.00010/) (2017)
- [Efficient Continuous Pareto Exploration in Multi-Task Learning](https://mlsanity.com/paper/2006.16434/) (2020)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [Average Individual Fairness: Algorithms, Generalization and Experiments](https://mlsanity.com/paper/1905.10607/) (2019)
- [A Short-term Intervention for Long-term Fairness in the Labor Market](https://mlsanity.com/paper/1712.00064/) (2017)
- [Fairness Under Composition](https://mlsanity.com/paper/1806.06122/) (2018)
- [The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally](https://mlsanity.com/paper/1910.04123/) (2019)
- [Fair Classification and Social Welfare](https://mlsanity.com/paper/1905.00147/) (2019)
- [Downstream Effects of Affirmative Action](https://mlsanity.com/paper/1808.09004/) (2018)
- [Efficient Fair Principal Component Analysis](https://mlsanity.com/paper/1911.04931/) (2019)

## Built on by (most cited first, 8 of 8)

- [Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set](https://mlsanity.com/paper/2110.08713/) (2021)
- [Optimization on Pareto sets: On a theory of multi-objective optimization](https://mlsanity.com/paper/2308.02145/) (2023)
- [Adaptive Distillation: Aggregating Knowledge from Multiple Paths for Efficient Distillation](https://mlsanity.com/paper/2110.09674/) (2021)
- [Generalization In Multi-Objective Machine Learning](https://mlsanity.com/paper/2208.13499/) (2022)
- [Adaptive Online Mirror Descent for Tchebycheff Scalarization in Multi-Objective Learning](https://mlsanity.com/paper/2410.21764/) (2024)
- [Enhancing Fairness and Performance in Machine Learning Models: A Multi-Task Learning Approach with Monte-Carlo Dropout and Pareto Optimality](https://mlsanity.com/paper/2404.08230/) (2024)
- [Audits Under Resource, Data, and Access Constraints: Scaling Laws For Less Discriminatory Alternatives](https://mlsanity.com/paper/2509.05627/) (2025)
- [Towards the Linear Algebra Based Taxonomy of XAI Explanations](https://mlsanity.com/paper/2301.13138/) (2023)

## Abstract (arXiv)

As algorithmic decision-making systems are becoming more pervasive, it is crucial to ensure such systems do not become mechanisms of unfair discrimination on the basis of gender, race, ethnicity, religion, etc. Moreover, due to the inherent trade-off between fairness measures and accuracy, it is desirable to learn fairness-enhanced models without significantly compromising the accuracy. In this paper, we propose Pareto efficient Fairness (PEF) as a suitable fairness notion for supervised learning, that can ensure the optimal trade-off between overall loss and other fairness criteria. The proposed PEF notion is definition-agnostic, meaning that any well-defined notion of fairness can be reduced to the PEF notion. To efficiently find a PEF classifier, we cast the fairness-enhanced classification as a bilevel optimization problem and propose a gradient-based method that can guarantee the solution belongs to the Pareto frontier with provable guarantees for convex and non-convex objectives. We also generalize the proposed algorithmic solution to extract and trace arbitrary solutions from the Pareto frontier for a given preference over accuracy and fairness measures. This approach is generic and can be generalized to any multicriteria optimization problem to trace points on the Pareto frontier curve, which is interesting by its own right. We empirically demonstrate the effectiveness of the PEF solution and the extracted Pareto frontier on real-world datasets compared to state-of-the-art methods.