Understanding Fairness Surrogate Functions in Algorithmic Fairness

TL;DR

This paper investigates the limitations of fairness surrogate functions in algorithmic fairness, revealing a gap between surrogate and true fairness, and proposes a sigmoid surrogate and a balanced algorithm to improve fairness and stability.

Contribution

It introduces a theoretical analysis of the surrogate-fairness gap, proposes a new sigmoid surrogate function, and develops the Balanced Surrogate algorithm to enhance fairness and stability.

Findings

The sigmoid surrogate reduces the surrogate-fairness gap.

The Balanced Surrogate algorithm iteratively mitigates unfairness.

Empirical results show improved fairness and stability with maintained accuracy.

Abstract

It has been observed that machine learning algorithms exhibit biased predictions against certain population groups. To mitigate such bias while achieving comparable accuracy, a promising approach is to introduce surrogate functions of the concerned fairness definition and solve a constrained optimization problem. However, it is intriguing in previous work that such fairness surrogate functions may yield unfair results and high instability. In this work, in order to deeply understand them, taking a widely used fairness definition--demographic parity as an example, we show that there is a surrogate-fairness gap between the fairness definition and the fairness surrogate function. Also, the theoretical analysis and experimental results about the gap motivate us that the fairness and stability will be affected by the points far from the decision boundary, which is the large margin points issue investigated in this paper. To address it, we propose the general sigmoid surrogate to simultaneously reduce both the surrogate-fairness gap and the variance, and offer a rigorous fairness and stability upper bound. Interestingly, the theory also provides insights into two important issues that deal with the large margin points as well as obtaining a more balanced dataset are beneficial to fairness and stability. Furthermore, we elaborate a novel and general algorithm called Balanced Surrogate, which iteratively reduces the gap to mitigate unfairness. Finally, we provide empirical evidence showing that our methods consistently improve fairness and stability while maintaining accuracy comparable to the baselines in three real-world datasets.