Fairness-Aware Optimization in Logistic Regression: Empirical Trade-Offs Across Healthcare and Socioeconomic Domains

Abstract

With the increased use of machine learning predictive models, there is a growing need to ensure algorithmic fairness and balance out inequality in predictive errors across various application domains, such as health care and income prediction. To make machine learning algorithms more useful and applicable in everyday settings, the issue of algorithmic fairness and the differences in error rates across groups has gained importance. While numerous efforts have been made to detect bias, very few studies consider the effect of incorporating explicit constraints into an optimization framework on the training process. This paper examines how the fairness regularization parameter (lambda) affects the predictive and fairness characteristics of logistic regression models trained via gradient descent. The experimental results were obtained using two datasets: the UCI Adult Income dataset, which is not a healthcare setting, and the UCI Heart Disease dataset, which is a healthcare setting. The experiment uses either demographic parity or an equal opportunity regularizer, along with cross-entropy loss for each model. To evaluate the results, the demographic parity difference and the equal opportunity difference are considered in addition to accuracy and AUC. The results show that fairness interventions are highly domain dependent: the same regularization strategy substantially improves fairness in large socioeconomic datasets but provides limited benefits in small healthcare datasets. In the Adult Income dataset, higher tuning parameter values led to lower fairness gaps and slightly increased accuracy; in the Heart Disease dataset, the gap improvement is smaller but accompanied by decreased performance. The findings highlight that fairness-aware optimization should be treated as a context-sensitive design choice rather than a universally transferable solution.