Understanding Fairness Surrogate Functions in Algorithmic Fairness

Wei Yao, Zhanke Zhou, Zhicong Li, Bo Han, Yong Liu

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.

Submission Length: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=5gelkVbjZb

Changes Since Last Submission:

Our last submission was desk rejected because of the font issue:

Desk Reject Comments:
Some fonts appear slightly modified from template default (e.g., title, "Abstract"). Please revisit and resubmit.

So we just modify the font and resubmit. The content has not been changed.

Assigned Action Editor: ~changjian_shui1

Submission Number: 2015