  Federated learning has attracted increasing attention due to the promise of
balancing privacy and large-scale learning; numerous approaches have been
proposed. However, most existing approaches focus on problems with balanced
data, and prediction performance is far from satisfactory for many real-world
applications where the number of samples in different classes is highly
imbalanced. To address this challenging problem, we developed a novel federated
learning method for imbalanced data by directly optimizing the area under curve
(AUC) score. In particular, we formulate the AUC maximization problem as a
federated compositional minimax optimization problem, develop a local
stochastic compositional gradient descent ascent with momentum algorithm, and
provide bounds on the computational and communication complexities of our
algorithm. To the best of our knowledge, this is the first work to achieve such
favorable theoretical results. Finally, extensive experimental results confirm
the efficacy of our method.
