Fairness Constraints: Mechanisms for Fair Classification

TL;DR

The paper tackles fairness in binary classification by introducing a convex, interpretable measure of decision boundary fairness, covariance between sensitive attributes and the signed distance to the boundary. It presents two convex optimization frameworks: one maximizing accuracy under fairness constraints to satisfy the p%-rule, and another maximizing fairness under accuracy constraints to honor business necessity. Through synthetic and real-data experiments, including Adult and Bank datasets, the authors demonstrate controllable fairness-accuracy trade-offs with minimal accuracy loss and show the method outperforms certain pre-processing and regularization baselines. The approach extends to multiple and non-binary sensitive attributes and provides a practical, scalable path toward compliant and fair decision-making in real-world systems.

Abstract

Algorithmic decision making systems are ubiquitous across a wide variety of online as well as offline services. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of the end user and profitability. However, there is a growing concern that these automated decisions can lead, even in the absence of intent, to a lack of fairness, i.e., their outcomes can disproportionately hurt (or, benefit) particular groups of people sharing one or more sensitive attributes (e.g., race, sex). In this paper, we introduce a flexible mechanism to design fair classifiers by leveraging a novel intuitive measure of decision boundary (un)fairness. We instantiate this mechanism with two well-known classifiers, logistic regression and support vector machines, and show on real-world data that our mechanism allows for a fine-grained control on the degree of fairness, often at a small cost in terms of accuracy.

Figures (7)

• Figure 1: The solid light blue lines show the decision boundaries for logistic regressors without fairness constraints. The dashed lines show the decision boundaries for fair logistic regressors trained (a) to maximize accuracy under fairness constraints and (b) to maximize fairness under fine-grained accuracy constraints, which prevents users with $z=1$ (circles) labeled as positive by the unconstrained classifier from being moved to the negative class. Each column corresponds to a dataset, with different correlation value between sensitive attribute values (crosses vs circles) and class labels (red vs green).
• Figure 2: [Maximizing accuracy under fairness constraints: single, binary sensitive attribute] Panels in (a) show the trade-off between the empirical covariance in Eq. \ref{['eq:fairness-definition']} and the relative loss (with respect to the unconstrained classifier), for the Adult (top) and Bank (bottom) datasets. Here each pair of (covariance, loss) values is guaranteed to be Pareto optimal by construction. Panels in (b) show the correspondence between the empirical covariance and the $p$%-rule for classifiers trained under fairness constraints. Panels in (c) show the accuracy against $p$%-rule value (top) and the percentage of protected (dashed) and non-protected (solid) users in the positive class against the $p$%-rule value (bottom).
• Figure 3: [Maximizing accuracy under fairness constraints: non-binary and several sensitive attributes] The figure shows accuracy (top) and percentage of users in positive class (bottom) against a multiplicative factor $a \in [0,1]$ such that $\mathbf{c} = a \mathbf{c}^{*}$, where $\mathbf{c}^{*}$ denotes the unconstrained classifier covariance.
• Figure 4: [Maximizing fairness under accuracy constraints] Panels in (a) show accuracy (solid) and $p$%-rule value (dashed) against $\gamma$. Panels in (b) show the percentage of protected (P, dashed) and non-protected (N-P, solid) users in the positive class against $\gamma$.
• Figure 5: Decision boundaries for SVM classifier with RBF Kernel trained without fairness constraints (left) and with fairness constraints ($\mathbf{c}=0$) on two synthetic datasets with different correlation value between sensitive attribute values (crosses vs circles) and class labels (red vs green).