  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 the
performance of the models on under-represented groups, as these parts of the
distribution are difficult to learn in the presence of noise. Existing
approaches for enforcing fairness in machine learning models have considered
the centralized setting, in which the algorithm has access to the users' data.
This paper introduces an algorithm to enforce group fairness in private
federated learning, where users' data does not leave their devices. First, the
paper extends the modified method of differential multipliers to empirical risk
minimization with fairness constraints, thus providing an algorithm to enforce
fairness in the central setting. Then, this algorithm is extended to the
private federated learning setting. The proposed algorithm, \texttt{FPFL}, is
tested on a federated version of the Adult dataset and an "unfair" version of
the FEMNIST dataset. The experiments on these datasets show how private
federated learning accentuates unfairness in the trained models, and how FPFL
is able to mitigate such unfairness.
