# Unleashing Linear Optimizers for Group-Fair Learning and Optimization

arXiv: https://arxiv.org/abs/1804.04503 · HTML: https://mlsanity.com/paper/1804.04503/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2018.

## Built on by (most cited first, 3 of 3)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [When Personalization Harms: Reconsidering the Use of Group Attributes in Prediction](https://mlsanity.com/paper/2206.02058/) (2022)
- [Class-attribute Priors: Adapting Optimization to Heterogeneity and Fairness Objective](https://mlsanity.com/paper/2401.14343/) (2024)

## Abstract (arXiv)

Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for example, when balancing performance or loss with fairness across people. We prove that, from a computational perspective, optimizing arbitrary objectives that take into account performance over a small number of groups is not significantly harder to optimize than average performance. Our main result is a polynomial-time reduction that uses a linear optimizer to optimize an arbitrary (Lipschitz continuous) function of performance over a (constant) number of possibly-overlapping groups. This includes fairness objectives over small numbers of groups, and we further point out that other existing notions of fairness such as individual fairness can be cast as convex optimization and hence more standard convex techniques can be used. Beyond learning, our approach applies to multi-objective optimization, more generally.