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.
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