Abstract

AUC (Area Under ROC Curve) has been an impor-tant criterion widely used in diverse learning tasks. To optimize AUC, many learning approaches have been developed, most working with pairwise surro-gate losses. Thus, it is important to study the AUC consistency based on minimizing pairwise surro-gate losses. In this paper, we introduce the general-ized calibration for AUC optimization, and prove that it is a necessary condition for AUC consis-tency. We then provide a sufficient condition for AUC consistency, and show its usefulness in study-ing the consistency of various surrogate losses, as well as the invention of new consistent losses. We further derive regret bounds for exponential and lo-gistic losses, and present regret bounds for more general surrogate losses in the realizable setting. Finally, we prove regret bounds that disclose the equivalence between the pairwise exponential loss of AUC and univariate exponential loss of accuracy. 1