  Multi-task learning (MTL) is a novel framework to learn several tasks
simultaneously with a single shared network where each task has its distinct
personalized header network for fine-tuning. MTL can be implemented in
federated learning settings as well, in which tasks are distributed across
clients. In federated settings, the statistical heterogeneity due to different
task complexities and data heterogeneity due to non-iid nature of local
datasets can both degrade the learning performance of the system. In addition,
tasks can negatively affect each other's learning performance due to negative
transference effects. To cope with these challenges, we propose FedGradNorm
which uses a dynamic-weighting method to normalize gradient norms in order to
balance learning speeds among different tasks. FedGradNorm improves the overall
learning performance in a personalized federated learning setting. We provide
convergence analysis for FedGradNorm by showing that it has an exponential
convergence rate. We also conduct experiments on multi-task facial landmark
(MTFL) and wireless communication system dataset (RadComDynamic). The
experimental results show that our framework can achieve faster training
performance compared to equal-weighting strategy. In addition to improving
training speed, FedGradNorm also compensates for the imbalanced datasets among
clients.
