# Stochastic Methods for AUC Optimization subject to AUC-based Fairness Constraints

arXiv: https://arxiv.org/abs/2212.12603 · HTML: https://mlsanity.com/paper/2212.12603/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 50 references that are in the map.
- First posted on arXiv 23 Dec 2022.

## Builds on (most cited first, 24 of 24)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Putting Fairness Principles into Practice: Challenges, Metrics, and Improvements](https://mlsanity.com/paper/1901.04562/) (2019)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [On Formalizing Fairness in Prediction with Machine Learning](https://mlsanity.com/paper/1710.03184/) (2017)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Algorithmic Fairness Datasets: the Story so Far](https://mlsanity.com/paper/2202.01711/) (2022)
- [The Fairness of Risk Scores Beyond Classification: Bipartite Ranking and the xAUC Metric](https://mlsanity.com/paper/1902.05826/) (2019)
- [Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimization](https://mlsanity.com/paper/1908.02734/) (2019)
- [Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints](https://mlsanity.com/paper/1908.01871/) (2019)
- [FairGBM: Gradient Boosting with Fairness Constraints](https://mlsanity.com/paper/2209.07850/) (2022)
- [First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Points](https://mlsanity.com/paper/2212.00927/) (2022)
- [Minimax AUC Fairness: Efficient Algorithm with Provable Convergence](https://mlsanity.com/paper/2208.10451/) (2022)
- [Adaptive Primal-Dual Stochastic Gradient Method for Expectation-constrained Convex Stochastic Programs](https://mlsanity.com/paper/2012.14943/) (2020)
- [Data-Driven Minimax Optimization with Expectation Constraints](https://mlsanity.com/paper/2202.07868/) (2022)
- [A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraints](https://mlsanity.com/paper/1908.03077/) (2019)
- [Stochastic Compositional Optimization with Compositional Constraints](https://mlsanity.com/paper/2209.04086/) (2022)

## Built on by (most cited first, 9 of 9)

- [Preserving AUC Fairness in Learning with Noisy Protected Groups](https://mlsanity.com/paper/2505.18532/) (2025)
- [Enabling Group Fairness in Graph Unlearning via Bi-level Debiasing](https://mlsanity.com/paper/2505.09702/) (2025)
- [Provable Optimization for Adversarial Fair Self-supervised Contrastive Learning](https://mlsanity.com/paper/2406.05686/) (2024)
- [Multi-Output Distributional Fairness via Post-Processing](https://mlsanity.com/paper/2409.00553/) (2024)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [AdFair-CLIP: Adversarial Fair Contrastive Language-Image Pre-training for Chest X-rays](https://mlsanity.com/paper/2506.23467/) (2025)
- [FairPOT: Balancing AUC Performance and Fairness with Proportional Optimal Transport](https://mlsanity.com/paper/2508.03940/) (2025)
- [Towards Size-invariant Salient Object Detection: A Generic Evaluation and Optimization Approach](https://mlsanity.com/paper/2509.15573/) (2025)
- [Mitigating Bias in Graph Hyperdimensional Computing](https://mlsanity.com/paper/2512.07433/) (2025)

## Abstract (arXiv)

As machine learning being used increasingly in making high-stakes decisions, an arising challenge is to avoid unfair AI systems that lead to discriminatory decisions for protected population. A direct approach for obtaining a fair predictive model is to train the model through optimizing its prediction performance subject to fairness constraints, which achieves Pareto efficiency when trading off performance against fairness. Among various fairness metrics, the ones based on the area under the ROC curve (AUC) are emerging recently because they are threshold-agnostic and effective for unbalanced data. In this work, we formulate the training problem of a fairness-aware machine learning model as an AUC optimization problem subject to a class of AUC-based fairness constraints. This problem can be reformulated as a min-max optimization problem with min-max constraints, which we solve by stochastic first-order methods based on a new Bregman divergence designed for the special structure of the problem. We numerically demonstrate the effectiveness of our approach on real-world data under different fairness metrics.