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.

翻译：本文针对深度学习中可应用的单向与双向部分AUC（pAUC）最大化问题，提出了系统且高效的基于梯度的方法。通过利用分布鲁棒优化（DRO）为每个正样本定义损失函数，我们提出了pAUC替代目标的新颖形式化方法。我们考虑了两种DRO形式：一种基于条件风险价值（CVaR），可生成非光滑但对pAUC精确的估计量；另一种基于KL散度正则化DRO，可生成非精确但对pAUC光滑（软性）的估计量。针对单向与双向pAUC最大化，我们分别提出两种算法，并证明其在优化各自形式时的收敛性。实验结果表明，所提算法在多种数据集上对深度学习pAUC最大化具有有效性。