# Using Property Elicitation to Understand the Impacts of Fairness Regularizers

arXiv: https://arxiv.org/abs/2309.11343 · HTML: https://mlsanity.com/paper/2309.11343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 14 of 14)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Privacy Regularization: Joint Privacy-Utility Optimization in Language Models](https://mlsanity.com/paper/2103.07567/) (2021)
- [Stable and Fair Classification](https://mlsanity.com/paper/1902.07823/) (2019)
- [An Embedding Framework for Consistent Polyhedral Surrogates](https://mlsanity.com/paper/1907.07330/) (2019)
- [Fair Generalized Linear Models with a Convex Penalty](https://mlsanity.com/paper/2206.09076/) (2022)
- [Fair Prediction with Endogenous Behavior](https://mlsanity.com/paper/2002.07147/) (2020)
- [Attainability and Optimality: The Equalized Odds Fairness Revisited](https://mlsanity.com/paper/2202.11853/) (2022)
- [Fairness Through Regularization for Learning to Rank](https://mlsanity.com/paper/2102.05996/) (2021)

## Abstract (arXiv)

Predictive algorithms are often trained by optimizing some loss function, to which regularization functions are added to impose a penalty for violating constraints. As expected, the addition of such regularization functions can change the minimizer of the objective. It is not well-understood which regularizers change the minimizer of the loss, and, when the minimizer does change, how it changes. We use property elicitation to take first steps towards understanding the joint relationship between the loss and regularization functions and the optimal decision for a given problem instance. In particular, we give a necessary and sufficient condition on loss and regularizer pairs for when a property changes with the addition of the regularizer, and examine some regularizers satisfying this condition standard in the fair machine learning literature. We empirically demonstrate how algorithmic decision-making changes as a function of both data distribution changes and hardness of the constraints.