# Understanding Fairness Surrogate Functions in Algorithmic Fairness

arXiv: https://arxiv.org/abs/2310.11211 · HTML: https://mlsanity.com/paper/2310.11211/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 83 references that are in the map.
- First posted on arXiv 17 Oct 2023.

## Builds on (most cited first, 30 of 48)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [DecodingTrust: A Comprehensive Assessment of Trustworthiness in GPT Models](https://mlsanity.com/paper/2306.11698/) (2023)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [A comparative study of fairness-enhancing interventions in machine learning](https://mlsanity.com/paper/1802.04422/) (2018)
- [Data-centric Artificial Intelligence: A Survey](https://mlsanity.com/paper/2303.10158/) (2023)
- [Summary of ChatGPT-Related Research and Perspective Towards the Future of Large Language Models](https://mlsanity.com/paper/2304.01852/) (2023)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Why Is My Classifier Discriminatory?](https://mlsanity.com/paper/1805.12002/) (2018)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [FairBatch: Batch Selection for Model Fairness](https://mlsanity.com/paper/2012.01696/) (2020)
- [A Survey on Fairness in Large Language Models](https://mlsanity.com/paper/2308.10149/) (2023)
- [Understanding the Origins of Bias in Word Embeddings](https://mlsanity.com/paper/1810.03611/) (2018)

## Built on by (most cited first, 8 of 8)

- [Is it Still Fair? A Comparative Evaluation of Fairness Algorithms through the Lens of Covariate Drift](https://mlsanity.com/paper/2409.12428/) (2024)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [ReLU integral probability metric and its applications](https://mlsanity.com/paper/2504.18897/) (2025)
- [A Flexible Fairness Framework with Surrogate Loss Reweighting for Addressing Sociodemographic Disparities](https://mlsanity.com/paper/2503.16836/) (2025)
- [Some Optimizers are More Equal: Understanding the Role of Optimizers in Group Fairness](https://mlsanity.com/paper/2504.14882/) (2025)
- [Fair Supervised Learning Through Constraints on Smooth Nonconvex Unfairness-Measure Surrogates](https://mlsanity.com/paper/2505.15788/) (2025)
- [FedFACT: A Provable Framework for Controllable Group-Fairness Calibration in Federated Learning](https://mlsanity.com/paper/2506.03777/) (2025)
- [Learning to Rank with Top-K Fairness](https://mlsanity.com/paper/2509.18067/) (2025)

## Abstract (arXiv)

It has been observed that machine learning algorithms exhibit biased predictions against certain population groups. To mitigate such bias while achieving comparable accuracy, a promising approach is to introduce surrogate functions of the concerned fairness definition and solve a constrained optimization problem. However, it is intriguing in previous work that such fairness surrogate functions may yield unfair results and high instability. In this work, in order to deeply understand them, taking a widely used fairness definition--demographic parity as an example, we show that there is a surrogate-fairness gap between the fairness definition and the fairness surrogate function. Also, the theoretical analysis and experimental results about the gap motivate us that the fairness and stability will be affected by the points far from the decision boundary, which is the large margin points issue investigated in this paper. To address it, we propose the general sigmoid surrogate to simultaneously reduce both the surrogate-fairness gap and the variance, and offer a rigorous fairness and stability upper bound. Interestingly, the theory also provides insights into two important issues that deal with the large margin points as well as obtaining a more balanced dataset are beneficial to fairness and stability. Furthermore, we elaborate a novel and general algorithm called Balanced Surrogate, which iteratively reduces the gap to mitigate unfairness. Finally, we provide empirical evidence showing that our methods consistently improve fairness and stability while maintaining accuracy comparable to the baselines in three real-world datasets.