  Multi-task learning (MTL) is a learning paradigm to learn multiple related
tasks simultaneously with a single shared network where each task has a
distinct personalized header network for fine-tuning. MTL can be integrated
into a federated learning (FL) setting if tasks are distributed across clients
and clients have a single shared network, leading to personalized federated
learning (PFL). To cope with statistical heterogeneity in the federated setting
across clients which can significantly degrade the learning performance, we use
a distributed dynamic weighting approach. To perform the communication between
the remote parameter server (PS) and the clients efficiently over the noisy
channel in a power and bandwidth-limited regime, we utilize over-the-air (OTA)
aggregation and hierarchical federated learning (HFL). Thus, we propose
hierarchical over-the-air (HOTA) PFL with a dynamic weighting strategy which we
call HOTA-FedGradNorm. Our algorithm considers the channel conditions during
the dynamic weight selection process. We conduct experiments on a wireless
communication system dataset (RadComDynamic). The experimental results
demonstrate that the training speed with HOTA-FedGradNorm is faster compared to
the algorithms with a naive static equal weighting strategy. In addition,
HOTA-FedGradNorm provides robustness against the negative channel effects by
compensating for the channel conditions during the dynamic weight selection
process.
