# Buffered AUC maximization for scoring systems via mixed-integer optimization

arXiv: https://arxiv.org/abs/2601.05544 · HTML: https://mlsanity.com/paper/2601.05544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 9 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Supersparse Linear Integer Models for Optimized Medical Scoring Systems](https://mlsanity.com/paper/1502.04269/) (2015)
- [Learning Optimized Risk Scores](https://mlsanity.com/paper/1610.00168/) (2016)
- [Interpretable Classification Models for Recidivism Prediction](https://mlsanity.com/paper/1503.07810/) (2015)
- [Learning Optimal Predictive Checklists](https://mlsanity.com/paper/2112.01020/) (2021)
- [Progress in Mathematical Programming Solvers from 2001 to 2020](https://mlsanity.com/paper/2206.09787/) (2022)
- [Scalable Holistic Linear Regression](https://mlsanity.com/paper/1902.03272/) (2019)
- [The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization](https://mlsanity.com/paper/1508.01922/) (2015)
- [Subset Selection for Multiple Linear Regression via Optimization](https://mlsanity.com/paper/1701.07920/) (2017)
- [A Mathematical Programming Approach for Integrated Multiple Linear Regression Subset Selection and Validation](https://mlsanity.com/paper/1712.04543/) (2017)

## Abstract (arXiv)

A scoring system is a linear classifier composed of a small number of explanatory variables, each assigned a small integer coefficient. This system is highly interpretable and allows predictions to be made with simple manual calculations without the need for a calculator. Several previous studies have used mixed-integer optimization (MIO) techniques to develop scoring systems for binary classification; however, they have not focused on directly maximizing AUC (i.e., area under the receiver operating characteristic curve), even though AUC is recognized as an essential evaluation metric for scoring systems. Our goal herein is to establish an effective MIO framework for constructing scoring systems that directly maximize the buffered AUC (bAUC) as the tightest concave lower bound on AUC. Our optimization model is formulated as a mixed-integer linear optimization (MILO) problem that maximizes bAUC subject to a group sparsity constraint for limiting the number of questions in the scoring system. Computational experiments using publicly available real-world datasets demonstrate that our MILO method can build scoring systems with superior AUC values compared to the baseline methods based on regularization and stepwise regression. This research contributes to the advancement of MIO techniques for developing highly interpretable classification models.