# A Comprehensive Review and Benchmarking of Fairness-Aware Variants of Machine Learning Models
## 3 Fair Editions of Decision Trees
### Optimal and Fair Decision Trees via Regularization (RegOCT)  
The authors of [7] proposed a Mixed Integer Programming (MIP) framework for learning optimal and fair Decision Trees, addressing both Disparate Treatment and Disparate Impact in decision-making processes. They introduced two additional fairness indices: the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Key Idea** & **Fairness Metric(s)** & **Datasets** & **Remarks** \\ \hline \multirow{4}{*}{Fair and Optimal Decision Trees [9]} & \multirow{4}{*}{Dynamic programming with pruning based on fairness bounds to improve scalability.} & \multirow{4}{*}{Bounds Based on Demographic Parity} & Adult, Bank Marketing, Communities and Crime, COMPAS, Dutch Census, German Credit, KDD Census, Census, OULAD, Ricci, Student-Mathematics/ Portuguese & \multirow{4}{*}{Outperforms FairOCT in runtime and scalability.} \\  & & & & \\ \cline{1-1} \cline{5-5}  & \multirow{4}{*}{Dynamic programming with pruning based on fairness bounds to improve scalability.} & \multirow{4}{*}{Bounds Based on Demographic Parity} & Adult, Bank Marketing, Communities and Crime, COMPAS, Dutch Census, German Credit, KDD Census, Census, OULAD, Ricci, Student-Mathematics/ Portuguese & \multirow{4}{*}{Outperforms FairOCT in runtime and scalability.} \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & \multirow{4}{*}{Allows user-defined combination of fairness constraints in splitting. Converts unfair nodes to leaves.} & \multirow{4}{*}{Demographic Parity, \(\,\)} & \multirow{4}{*}{Adult, Loan Granting} & Select more than one Fairness Metric Maintains accuracy and interpretability with fairness flexibility. \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & \multirow{4}{*}{Flow-based MIO with binary fairness constraints on paths and structure.} & \multirow{4}{*}{Statistical Parity, Conditional Statistical Parity, Equalized Odds} & COMPAS, Adult, German Credit & High interpretability and near-perfect fairness \\ \cline{1-1} \cline{5-5}  & & & & 4.2\% accuracy trade-off. \\ \hline \multirow{4}{*}{FAir-C4.5 [12]} & \multirow{4}{*}{Extension of C4.5 with fairness-aware attribute selection: Lexicographic, Constraint-Based, Gain Ratio-Fairness (GRXFR).} & \multirow{4}{*}{Disparate Impact} & Adult, German Credit, Propublica Recidivism, NYPD SQF CPW, Student Mathematics/Portuguese, More efficient than C4.5 & \multirow{4}{*}{0.5-2\% lower accuracy than C4.5} \\ \cline{1-1} \cline{5-5}  & \multirow{4}{*}{New splitting criterion (SCAFF) using ROC-AUC and demographic parity.} & \multirow{4}{*}{Demographic Parity} & \multirow{4}{*}{COMPAS, Adult} & \multirow{4}{*}{0.5-2\% lower accuracy than C4.5} \\ \cline{1-1} \cline{5-5}  & & & & \\ \cline{1-1} \cline{5-5}  & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._Disparate Impact Discrimination Index (DIDI), which quantifies classification bias, and the Disparate Treatment Discrimination Index (DTDI), which assesses individual fairness violations. The framework formulates Decision Tree optimization using linear programming constraints, with an objective function that balances classification accuracy (minimizing misclassification) and fairness constraints (reducing Disparate Impact and Disparate Treatment). The authors evaluated their approach on classification and regression tasks using real-world datasets, including Credit, Adult Income, COMPAS, and Crime. The results demonstrate that the proposed method achieves near-zero discrimination across these datasets, outperforming other fairness-aware Decision Trees such as the Discrimination-Aware Decision Tree, while maintaining minimal accuracy loss (1-3%) compared to CART and other heuristic-based models.