  In this paper, we propose systematic and efficient gradient-based methods for
both one-way and two-way partial AUC (pAUC) maximization that are applicable to
deep learning. We propose new formulations of pAUC surrogate objectives by
using the distributionally robust optimization (DRO) to define the loss for
each individual positive data. We consider two formulations of DRO, one of
which is based on conditional-value-at-risk (CVaR) that yields a non-smooth but
exact estimator for pAUC, and another one is based on a KL divergence
regularized DRO that yields an inexact but smooth (soft) estimator for pAUC.
For both one-way and two-way pAUC maximization, we propose two algorithms and
prove their convergence for optimizing their two formulations, respectively.
Experiments demonstrate the effectiveness of the proposed algorithms for pAUC
maximization for deep learning on various datasets.
