  Area under ROC curve (AUC) is a widely used performance measure for
classification models. We propose two new distributionally robust AUC
maximization models (DR-AUC) that rely on the Kantorovich metric and
approximate the AUC with the hinge loss function. We consider the two cases
with respectively fixed and variable support for the worst-case distribution.
We use duality theory to reformulate the DR-AUC models and derive tractable
convex optimization problems. The numerical experiments show that the proposed
DR-AUC models -- benchmarked with the standard deterministic AUC and the
support vector machine models - perform better in general and in particular
improve the worst-case out-of-sample performance over the majority of the
considered datasets, thereby showing their robustness. The results are
particularly encouraging since our numerical experiments are conducted with
training sets of small size which have been known to be conducive to low
out-of-sample performance.
