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Federated learning with differential privacy, or private federated learning,provides a strategy to train machine learning models while respecting users'privacy. However, differential privacy can disproportionately degrade theperformance of the models on under-represented groups, as these parts of thedistribution are difficult to learn in the presence of noise. Existingapproaches for enforcing fairness in machine learning models have consideredthe centralized setting, in which the algorithm has access to the users' data.This paper introduces an algorithm to enforce group fairness in privatefederated learning, where users' data does not leave their devices. First, thepaper extends the modified method of differential multipliers to empirical riskminimization with fairness constraints, thus providing an algorithm to enforcefairness in the central setting. Then, this algorithm is extended to theprivate federated learning setting. The proposed algorithm, \texttt{FPFL}, istested on a federated version of the Adult dataset and an "unfair" version ofthe FEMNIST dataset. The experiments on these datasets show how privatefederated learning accentuates unfairness in the trained models, and how FPFLis able to mitigate such unfairness.

Enforcing fairness in private federated learning via the modified method of differential multipliers