Demystifying the Optimal Fair Classifier in Multi-Class Classification

Ensuring fair and equitable treatment across diverse groups, particularly in multi-class classification tasks, poses a significant challenge due to the persistent biases inherent in machine learning models. Most existing bias mitigation techniques are tailored to binary settings, and the presence of multi-dimensional outputs and complex fairness mechanisms makes their extension to multi-class scenarios neither straightforward nor effective. In this paper, we investigate two fundamental, unresolved challenges in fair classification: (i) characterizing the optimal accuracy-fairness frontier in multi-class settings , and (ii) designing practical algorithms that attain this optimum across different training phases . To tackle these challenges, we first specify an analytically tractable probabilistic formulation of the optimal classifier under fairness constraints. Building upon this, we propose two attribute-blind algorithms to enforce fairness requirements in practice: an in-processing approach for fairness intervention during training via the reduction approach, and a post-processing approach for fine-tuning output probabilities with plug-in estimation. Theoretical analysis reveals that both methods converge to the optimal accuracy-fairness Pareto frontier. Experiments conducted on multiple datasets demonstrate the superior performance of our methods in balancing accuracy and fairness.