Correcting Overparameterization Effects in Fair Empirical Risk Minimization

Bias mitigation is particularly challenging for overparameterized machine learning (ML) models. Overfitting of training points not only amplifies data bias induced by spurious correlations, but also causes the failure of usual bias mitigation methods. To provide actionable insights to address this challenge, we propose a precise analysis of fair empirical risk minimization (ERM) in the overparameterized regime. Importantly, we show that even though conventional fair ERM fails on overparameterized models, this approach can be corrected by modifying the equality fairness constraint to allow for bias overcompensation. Moreover, our analysis presents an empirical criterion for strong equalized odds: balanced group-conditional means of representer coefficients, indicating equal average contribution from each sensitive group. Motivated by this result, we provide an estimable search interval that localizes the required overcompensation level for balanced coefficients. Despite the asymptotic nature of our findings, they closely capture the statistical behavior of moderately large ML models.

Our paper investigates why ensuring fair predictions across different subpopulations is difficult in very large machine learning models, and how to address this challenge. Large models often “overfit,” meaning they memorize training data rather than learning general patterns. When the data contains biases (for example, links between a sensitive trait and an outcome), overfitting can amplify those biases and cause standard fairness methods to fail. We analyse a common method called fair empirical risk minimization that optimizes the prediction error under certain fairness constraints on the training data, and show that it fails on large models due to the memorization of training data. Our main solution is to intentionally “overcompensate” for bias. Instead of enforcing strict equality between groups, the model should be pushed slightly in the opposite direction to counter hidden bias—similar to over-correcting when adjusting something misaligned. We also identify a practical signal of fairness: different groups should contribute equally, on average, to the model’s predictions. Based on this, we propose a way to estimate how much overcompensation is needed.