# Large-scale Optimization of Partial AUC in a Range of False Positive Rates

arXiv: https://arxiv.org/abs/2203.01505 · HTML: https://mlsanity.com/paper/2203.01505/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 88 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 28 of 28)

- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Large-scale Robust Deep AUC Maximization: A New Surrogate Loss and Empirical Studies on Medical Image Classification](https://mlsanity.com/paper/2012.03173/) (2020)
- [Weakly-Convex Concave Min-Max Optimization: Provable Algorithms and Applications in Machine Learning](https://mlsanity.com/paper/1810.02060/) (2018)
- [Efficiency of minimizing compositions of convex functions and smooth maps](https://mlsanity.com/paper/1605.00125/) (2016)
- [Learning with Average Top-k Loss](https://mlsanity.com/paper/1705.08826/) (2017)
- [Learning with Multiclass AUC: Theory and Algorithms](https://mlsanity.com/paper/2107.13171/) (2021)
- [First-order Convergence Theory for Weakly-Convex-Weakly-Concave Min-max Problems](https://mlsanity.com/paper/1810.10207/) (2018)
- [Stochastic subgradient method converges at the rate O(k-1/4) on weakly convex functions](https://mlsanity.com/paper/1802.02988/) (2018)
- [Minimizing the Maximal Loss: How and Why?](https://mlsanity.com/paper/1602.01690/) (2016)
- [Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems](https://mlsanity.com/paper/1707.03505/) (2017)
- [When AUC meets DRO: Optimizing Partial AUC for Deep Learning with Non-Convex Convergence Guarantee](https://mlsanity.com/paper/2203.00176/) (2022)
- [Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization](https://mlsanity.com/paper/1306.4650/) (2013)
- [Learning by Minimizing the Sum of Ranked Range](https://mlsanity.com/paper/2010.01741/) (2020)
- [Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints](https://mlsanity.com/paper/1908.01871/) (2019)
- [Online and Stochastic Gradient Methods for Non-decomposable Loss Functions](https://mlsanity.com/paper/1410.6776/) (2014)
- [Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence](https://mlsanity.com/paper/1811.11829/) (2018)
- [Convergence guarantees for a class of non-convex and non-smooth optimization problems](https://mlsanity.com/paper/1804.09629/) (2018)
- [Computing B-Stationary Points of Nonsmooth DC Programs](https://mlsanity.com/paper/1511.01796/) (2015)
- [Support Vector Algorithms for Optimizing the Partial Area Under the ROC Curve](https://mlsanity.com/paper/1605.04337/) (2016)
- [A proximal difference-of-convex algorithm with extrapolation](https://mlsanity.com/paper/1612.06265/) (2016)
- [Two-Way Partial AUC and Its Properties](https://mlsanity.com/paper/1508.00298/) (2015)
- [On the rate of convergence of the Difference-of-Convex Algorithm (DCA)](https://mlsanity.com/paper/2109.13566/) (2021)
- [Accelerating the DC algorithm for smooth functions](https://mlsanity.com/paper/1507.07375/) (2015)
- [Partial AUC Maximization via Nonlinear Scoring Functions](https://mlsanity.com/paper/1806.04838/) (2018)
- [Efficiency of Coordinate Descent Methods For Structured Nonconvex Optimization](https://mlsanity.com/paper/1909.00918/) (2019)
- [Online Stochastic DCA with applications to Principal Component Analysis](https://mlsanity.com/paper/2108.02300/) (2021)
- [Convergence Analysis of a Proximal Point Algorithm for Minimizing Differences of Functions](https://mlsanity.com/paper/1504.08079/) (2015)
- [Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems](https://mlsanity.com/paper/1911.04334/) (2019)

## Built on by (most cited first, 15 of 15)

- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Lower-Left Partial AUC: An Effective and Efficient Optimization Metric for Recommendation](https://mlsanity.com/paper/2403.00844/) (2024)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Algorithmic Foundations of Empirical X-risk Minimization](https://mlsanity.com/paper/2206.00439/) (2022)
- [Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm](https://mlsanity.com/paper/2210.03967/) (2022)
- [Single-Loop Stochastic Algorithms for Difference of Max-Structured Weakly Convex Functions](https://mlsanity.com/paper/2405.18577/) (2024)
- [DRAUC: An Instance-wise Distributionally Robust AUC Optimization Framework](https://mlsanity.com/paper/2311.03055/) (2023)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [AUC Optimization from Multiple Unlabeled Datasets](https://mlsanity.com/paper/2305.15776/) (2023)
- [FairPOT: Balancing AUC Performance and Fairness with Proportional Optimal Transport](https://mlsanity.com/paper/2508.03940/) (2025)
- [Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations](https://mlsanity.com/paper/2512.01213/) (2025)
- [Statistical Robustness of Interval CVaR Based Regression Models under Perturbation and Contamination](https://mlsanity.com/paper/2601.11420/) (2026)
- [MoSSP: A Momentum-Based Single-Loop Stochastic Penalty Method for Nonconvex Constrained DC-Regularized Optimization](https://mlsanity.com/paper/2605.29635/) (2026)
- [Partial AUC Maximization from Positive-unlabeled Data](https://mlsanity.com/paper/2610.00284/) (2026)

## Abstract (arXiv)

The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of tilde O(1/ε6) for finding a nearly ε-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms for both partial AUC maximization and sum of ranked range loss minimization.