Constrained Optimisation for Fairness in Multi-Class Classification

The growing deployment of machine learning in sensitive domains such as healthcare, finance, education, and criminal justice has made algorithmic fairness a central concern: biased classifiers can systematically disadvantage individuals based on protected attributes like gender, race, or age. Correcting this without sacrificing predictive accuracy remains largely open, especially beyond simple binary decisions. Bias mitigation methods are generally grouped into three families depending on when they act in the ML pipeline: pre-processing approaches, which correct the training data before learning; post-processing approaches, which adjust an already-trained model's predictions; and in-processing approaches, which embed the fairness objective directly into the training process itself. Most existing methods, of all three kinds, were designed only for binary classification, leaving multi-class settings underexplored despite their frequent use in fields like education and healthcare. In this talk, I will present Generalised Exponentiated Gradient (GEG), a new method that, as an in-processing approach, has the advantage of directly shaping the model's decision boundary during learning rather than correcting it after the fact. GEG extends the reductions approach of Agarwal et al., originally formulated as a convex-concave saddle-point game between a learner and an auditor, to handle (i) multi-class label spaces and (ii) multiple fairness definitions enforced simultaneously, while preserving convexity and convergence guarantees. I will present extensive numerical results on ten real-world datasets, benchmarked against six baseline methods, showing that GEG consistently improves fairness with little to no loss in accuracy.