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, an intriguing issue in previous work is that such fairness surrogate functions may yield unfair results. In this work, in order to deeply understand this issue, taking a widely used fairness definition, demographic parity as an example, we both theoretically and empirically show that there is a surrogate-fairness gap between the fairness definition and the fairness surrogate function. The "gap" directly determines whether a surrogate function is an appropriate substitute for a fairness definition. Also, the theoretical analysis and experimental results about the "gap" motivate us that the unbounded surrogate functions 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 with a rigorous and reliable fairness guarantee. 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. Furthermore, we elaborate a novel and general algorithm called Balanced Surrogate, which iteratively reduces the "gap" to improve fairness. Finally, we provide empirical evidence showing that our methods achieve better fairness performance in three real-world datasets.

翻译：已观察到机器学习算法对某些人群存在有偏预测。为了在保持相当准确性的同时减轻这种偏差，一种有前景的方法是引入所关注公平性定义的代理函数，并求解约束优化问题。然而，以往工作中一个值得关注的问题是，这类公平代理函数可能产生不公平的结果。为深入理解该问题，本文以广泛使用的公平性定义——人口统计学平权为例，从理论和实证两方面证明公平性定义与公平代理函数之间存在代理-公平性差距。该"差距"直接决定代理函数是否适合替代公平性定义。同时，关于该"差距"的理论分析与实验结果促使我们认识到，无界代理函数将受到远离决策边界点的影响，即本文研究的大边界点问题。为解决此问题，我们提出具有严谨可靠公平性保证的通用S型代理函数。有趣的是，该理论还为两个重要问题提供了洞见：处理大边界点以及获取更均衡的数据集均有助于提升公平性。此外，我们详细阐述了一种新颖且通用的算法——平衡代理，该算法通过迭代缩小"差距"来改善公平性。最后，我们通过实验证据表明，我们的方法在三个真实世界数据集上实现了更优的公平性表现。