Federated Learning (FL) has emerged as a promising solution in Edge Computing (EC) environments to process the proliferation of data generated by edge devices. By collaboratively optimizing the global machine learning models on distributed edge devices, FL circumvents the need for transmitting raw data and enhances user privacy. Despite practical successes, FL still confronts significant challenges including constrained edge device resources, multiple tasks deployment, and data heterogeneity. However, existing studies focus on mitigating the FL training costs of each single task whereas neglecting the resource consumption across multiple tasks in heterogeneous FL scenarios. In this paper, we propose Heterogeneous Federated Learning with Local Parameter Sharing (FedLPS) to fill this gap. FedLPS leverages principles from transfer learning to facilitate the deployment of multiple tasks on a single device by dividing the local model into a shareable encoder and task-specific encoders. To further reduce resource consumption, a channel-wise model pruning algorithm that shrinks the footprint of local models while accounting for both data and system heterogeneity is employed in FedLPS. Additionally, a novel heterogeneous model aggregation algorithm is proposed to aggregate the heterogeneous predictors in FedLPS. We implemented the proposed FedLPS on a real FL platform and compared it with state-of-the-art (SOTA) FL frameworks. The experimental results on five popular datasets and two modern DNN models illustrate that the proposed FedLPS significantly outperforms the SOTA FL frameworks by up to 4.88% and reduces the computational resource consumption by 21.3%. Our code is available at:https://github.com/jyzgh/FedLPS.

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