Online AUC Optimization Based on Second-order Surrogate Loss
This work addresses the problem of efficient AUC optimization for large-scale, class-imbalanced classification tasks, representing a novel paradigm rather than an incremental improvement.
The paper tackled the challenge of optimizing AUC in class-imbalanced classification by proposing a novel second-order surrogate loss and an efficient online algorithm, achieving a tighter O(ln T) regret bound compared to the typical O(sqrt(T)) bound of existing methods.
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.