On Convexity and Bounds of Fairness-aware Classification

In this paper, we study the fairness-aware classification problem by formulating it as a constrained optimization problem. Several limitations exist in previous works due to the lack of a theoretical framework for guiding the formulation. We propose a general fairness-aware framework to address previous limitations. Our framework provides: (1) various fairness metrics that can be incorporated into classic classification models as constraints; (2) the convex constrained optimization problem that can be solved efficiently; and (3) the lower and upper bounds of real-world fairness measures that are established using surrogate functions, providing a fairness guarantee for constrained classifiers. Within the framework, we propose a constraint-free criterion under which any learned classifier is guaranteed to be fair in terms of the specified fairness metric. If the constraint-free criterion fails to satisfy, we further develop the method based on the bounds for constructing fair classifiers. The experiments using real-world datasets demonstrate our theoretical results and show the effectiveness of the proposed framework.