Online AUC Optimization Based on Second-order Surrogate Loss

• URL: http://arxiv.org/abs/2510.21202v1
• Date: Fri, 24 Oct 2025 07:08:22 GMT
• Title: Online AUC Optimization Based on Second-order Surrogate Loss
• Authors: JunRu Luo, Difei Cheng, Bo Zhang,
• Abstract summary: The Area Under the Curve is an important performance metric for classification tasks.<n>We develop a novel second-order surrogate loss based on the pairwise hinge loss, and an efficient online storage.<n>Our approach introduces a new paradigm that directly substitutes the entire aggregated pairwise loss with a loss function constructed from the first- and second-order statistics.
• Score: 3.9269332672496424
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Area Under the Curve (AUC) is an important performance metric for classification tasks, particularly in class-imbalanced scenarios. However, minimizing the AUC presents significant challenges due to the non-convex and discontinuous nature of pairwise 0/1 losses, which are difficult to optimize, as well as the substantial memory cost of instance-wise storage, which creates bottlenecks in large-scale applications. To overcome these challenges, we propose a novel second-order surrogate loss based on the pairwise hinge loss, and develop an efficient online algorithm. Unlike conventional approaches that approximate each individual pairwise 0/1 loss term with an instance-wise surrogate function, our approach introduces a new paradigm that directly substitutes the entire aggregated pairwise loss with a surrogate loss function constructed from the first- and second-order statistics of the training data. Theoretically, while existing online AUC optimization algorithms typically achieve an $\mathcal{O}(\sqrt{T})$ regret bound, our method attains a tighter $\mathcal{O}(\ln T)$ bound. Furthermore, we extend the proposed framework to nonlinear settings through a kernel-based formulation. Extensive experiments on multiple benchmark datasets demonstrate the superior efficiency and effectiveness of the proposed second-order surrogate loss in optimizing online AUC performance.

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