Understanding Fairness Surrogate Functions in Algorithmic Fairness
This addresses fairness and stability issues in machine learning algorithms for biased predictions against population groups, representing an incremental improvement with novel theoretical insights.
The paper tackles the problem that fairness surrogate functions in algorithmic fairness can yield unfair results and high instability, showing there's a surrogate-fairness gap and that large margin points affect fairness and stability. The result is a proposed general sigmoid surrogate and Balanced Surrogate algorithm that improve fairness and stability while maintaining comparable accuracy in three real-world datasets.
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.