# Learning Optimal Fair Classification Trees: Trade-offs Between Interpretability, Fairness, and Accuracy

arXiv: https://arxiv.org/abs/2201.09932 · HTML: https://mlsanity.com/paper/2201.09932/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 64 references that are in the map.
- First posted on arXiv 24 Jan 2022.

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

- [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)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [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)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Fairness Under Unawareness: Assessing Disparity When Protected Class Is Unobserved](https://mlsanity.com/paper/1811.11154/) (2018)
- [On the Existence of Simpler Machine Learning Models](https://mlsanity.com/paper/1908.01755/) (2019)
- [Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making](https://mlsanity.com/paper/1903.10598/) (2019)
- [FAHT: An Adaptive Fairness-aware Decision Tree Classifier](https://mlsanity.com/paper/1907.07237/) (2019)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [In Pursuit of Interpretable, Fair and Accurate Machine Learning for Criminal Recidivism Prediction](https://mlsanity.com/paper/2005.04176/) (2020)
- [Strong Optimal Classification Trees](https://mlsanity.com/paper/2103.15965/) (2021)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [Enforcing Interpretability and its Statistical Impacts: Trade-offs between Accuracy and Interpretability](https://mlsanity.com/paper/2010.13764/) (2020)
- [Fair Adversarial Gradient Tree Boosting](https://mlsanity.com/paper/1911.05369/) (2019)
- [Learning Optimal Prescriptive Trees from Observational Data](https://mlsanity.com/paper/2108.13628/) (2021)
- [Fair Training of Decision Tree Classifiers](https://mlsanity.com/paper/2101.00909/) (2021)
- [Fairness-guided SMT-based Rectification of Decision Trees and Random Forests](https://mlsanity.com/paper/2011.11001/) (2020)

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

- [Learning a Decision Tree Algorithm with Transformers](https://mlsanity.com/paper/2402.03774/) (2024)
- [SORTeD Rashomon Sets of Sparse Decision Trees: Anytime Enumeration](https://mlsanity.com/paper/2511.03344/) (2025)
- [Engineering the Law-Machine Learning Translation Problem: Developing Legally Aligned Models](https://mlsanity.com/paper/2504.16969/) (2025)
- [ODTlearn: A Package for Learning Optimal Decision Trees for Prediction and Prescription](https://mlsanity.com/paper/2307.15691/) (2023)
- [Learning Optimal Classification Trees Robust to Distribution Shifts](https://mlsanity.com/paper/2310.17772/) (2023)
- [Privacy Constrained Fairness Estimation for Decision Trees](https://mlsanity.com/paper/2312.08413/) (2023)
- [Fair and Accurate Regression: Strong Formulations and Algorithms](https://mlsanity.com/paper/2412.17116/) (2024)
- [A Multi-Objective Evaluation Framework for Analyzing Utility-Fairness Trade-Offs in Machine Learning Systems](https://mlsanity.com/paper/2503.11120/) (2025)
- [Symbolic Quantile Regression for the Interpretable Prediction of Conditional Quantiles](https://mlsanity.com/paper/2508.08080/) (2025)
- [Intersectional Fairness via Mixed-Integer Optimization](https://mlsanity.com/paper/2601.19595/) (2026)
- [PACE: Prune-And-Compress Ensemble Models](https://mlsanity.com/paper/2605.06278/) (2026)
- [Is Machine Learning Unsafe and Irresponsible in Social Sciences? Paradoxes and Reconsidering from Recidivism Prediction Tasks](https://mlsanity.com/paper/2311.06537/) (2023)
- [FairUDT: Fairness-aware Uplift Decision Trees](https://mlsanity.com/paper/2502.01188/) (2025)
- [A Unified Optimization Framework for Multiclass Classification with Structured Hyperplane Arrangements](https://mlsanity.com/paper/2510.05047/) (2025)
- [FairMed-XGB: A Bayesian-Optimised Multi-Metric Framework with Explainability for Demographic Equity in Critical Healthcare Data](https://mlsanity.com/paper/2603.14947/) (2026)

## Abstract (arXiv)

The increasing use of machine learning in high-stakes domains -- where people's livelihoods are impacted -- creates an urgent need for interpretable, fair, and highly accurate algorithms. With these needs in mind, we propose a mixed integer optimization (MIO) framework for learning optimal classification trees -- one of the most interpretable models -- that can be augmented with arbitrary fairness constraints. In order to better quantify the "price of interpretability", we also propose a new measure of model interpretability called decision complexity that allows for comparisons across different classes of machine learning models. We benchmark our method against state-of-the-art approaches for fair classification on popular datasets; in doing so, we conduct one of the first comprehensive analyses of the trade-offs between interpretability, fairness, and predictive accuracy. Given a fixed disparity threshold, our method has a price of interpretability of about 4.2 percentage points in terms of out-of-sample accuracy compared to the best performing, complex models. However, our method consistently finds decisions with almost full parity, while other methods rarely do.