Any news on this? I think differentiable objective functions that directly optimize ROC-AUC and PRC-AUC scores will be useful in many scenarios.
There are some paper describing such functions:
ROC-AUC: Optimizing Classifier Performance via an Approximation to the Wilcoxon-Mann-Whitney Statistic 8 (ICML 2003)
Paper (NIPS 2003)
PRC-AUC: [1608.04802] Scalable Learning of Non-Decomposable Objectives 3 (ICML 2016)