  Traditional federated optimization methods perform poorly with heterogeneous
data (ie, accuracy reduction), especially for highly skewed data. In this
paper, we investigate the label distribution skew in FL, where the distribution
of labels varies across clients. First, we investigate the label distribution
skew from a statistical view. We demonstrate both theoretically and empirically
that previous methods based on softmax cross-entropy are not suitable, which
can result in local models heavily overfitting to minority classes and missing
classes. Additionally, we theoretically introduce a deviation bound to measure
the deviation of the gradient after local update. At last, we propose FedLC
(\textbf {Fed} erated learning via\textbf {L} ogits\textbf {C} alibration),
which calibrates the logits before softmax cross-entropy according to the
probability of occurrence of each class. FedLC applies a fine-grained
calibrated cross-entropy loss to local update by adding a pairwise label
margin. Extensive experiments on federated datasets and real-world datasets
demonstrate that FedLC leads to a more accurate global model and much improved
performance. Furthermore, integrating other FL methods into our approach can
further enhance the performance of the global model.
