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

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.