Stochastic Primal-Dual Double Block-Coordinate for Two- way Partial AUC Maximization

Linli Zhou, Bokun Wang, My T. Thai, Tianbao Yang

Abstract: Two-way partial AUC (TPAUC) is a critical performance metric for binary classification with imbalanced data, as it focuses on specific ranges of the true positive rate (TPR) and false positive rate (FPR). However, stochastic algorithms for TPAUC optimization remain under-explored, with existing methods either limited to approximated TPAUC loss functions or burdened by sub-optimal complexities. To overcome these limitations, we introduce two innovative stochastic primal-dual double block-coordinate algorithms for TPAUC maximization. These algorithms utilize stochastic block-coordinate updates for both the primal and dual variables, catering to both convex and non-convex settings. We provide theoretical convergence rate analyses, demonstrating significant improvements over prior approaches. Our experimental results, based on multiple benchmark datasets, validate the superior performance of our algorithms, showcasing faster convergence and better generalization. This work advances the state of the art in TPAUC optimization and offers practical tools for real-world machine learning applications.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

In response to Reviewer YBcz’s feedback on related work, we have revised the introduction and related work section. Specifically:
1. We highlighted not only why existing methods yield inferior results but also the technical challenges they leave unresolved.
2. We emphasized our key ideas and contributions, clarifying how they address these challenges and advance the state of the art.

In addition, we improved the overall presentation and organization. We revised the proof of Lemma C.8 (Appendix C.3.2) to enhance readability. We strengthened the description of the technical novelty of our proposed methods to make the contributions more explicit.

Assigned Action Editor: ~Bo_Dai1

Submission Number: 4967