Pairwise AUC Optimization Needs Corrective Power: A Unified View

Jia Chen, Zhiyong Yang, Shilong Bao, Qianqian Xu, Qingming Huang

Direct pairwise AUC-surrogate training is attractive because it trains toward the ranking metric used at test time, especially under class imbalance. This creates a direct alignment between the training objective and the evaluation metric, but such metric alignment alone does not guarantee that stochastic training remains corrective. We study this gap through Corrective Power: whether pairwise mini-batch updates produce stronger and more reliable improvements for more severe positive-negative ranking errors. Our main observation is that direct pairwise training can enter regions where severe errors remain common but no longer produce useful corrective motion. In such regions, even the mini-batch noise that would normally help SGD move along the steepest severe-error correction direction can become much weaker. In this paper, we seek a theoretical explanation for this by exploring the degenerate property of the U-statistics formed from the pairwise gradients therein. Our results provide a mechanistic explanation for several empirical patterns: (a) squared-hinge loss is often an effective AUC surrogate; (b) cross-entropy warm-up can help models that enter the AUC phase from a poor…