"You Can't Fix What You Can't Measure": Privately Measuring Demographic Performance Disparities in Federated Learning

Federated learning allows many devices to collaborate in the training of machine learning models. As in traditional machine learning, there is a growing concern that models trained with federated learning may exhibit disparate performance for different demographic groups. Existing solutions to measure and ensure equal model performance across groups require access to information about group membership, but this access is not always available or desirable, especially under the privacy aspirations of federated learning. We study the feasibility of measuring such performance disparities while protecting the privacy of the user's group membership and the federated model's performance on the user's data. Protecting both is essential for privacy, because they may be correlated, and thus learning one may reveal the other. On the other hand, from the utility perspective, the privacy-preserved data should maintain the correlation to ensure the ability to perform accurate measurements of the performance disparity. We achieve both of these goals by developing locally differentially private mechanisms that preserve the correlations between group membership and model performance. To analyze the effectiveness of the mechanisms, we bound their error in estimating the disparity when optimized for a given privacy budget, and validate these bounds on synthetic data. Our results show that the error rapidly decreases for realistic numbers of participating clients, demonstrating that, contrary to what prior work suggested, protecting the privacy of protected attributes is not necessarily in conflict with identifying disparities in the performance of federated models.