  The use of machine learning models in consequential decision making often
exacerbates societal inequity, in particular yielding disparate impact on
members of marginalized groups defined by race and gender. The area under the
ROC curve (AUC) is widely used to evaluate the performance of a scoring
function in machine learning, but is studied in algorithmic fairness less than
other performance metrics. Due to the pairwise nature of the AUC, defining an
AUC-based group fairness metric is pairwise-dependent and may involve both
\emph{intra-group} and \emph{inter-group} AUCs. Importantly, considering only
one category of AUCs is not sufficient to mitigate unfairness in AUC
optimization. In this paper, we propose a minimax learning and bias mitigation
framework that incorporates both intra-group and inter-group AUCs while
maintaining utility. Based on this Rawlsian framework, we design an efficient
stochastic optimization algorithm and prove its convergence to the minimum
group-level AUC. We conduct numerical experiments on both synthetic and
real-world datasets to validate the effectiveness of the minimax framework and
the proposed optimization algorithm.
