Federated learning is an approach to collaboratively training machine learning models for multiple parties that prohibit data sharing. One of the challenges in federated learning is non-IID data between clients, as a single model can not fit the data distribution for all clients. Meta-learning, such as Per-FedAvg, is introduced to cope with the challenge. Meta-learning learns shared initial parameters for all clients. Each client employs gradient descent to adapt the initialization to local data distributions quickly to realize model personalization. However, due to non-convex loss function and randomness of sampling update, meta-learning approaches have unstable goals in local adaptation for the same client. This fluctuation in different adaptation directions hinders the convergence in meta-learning. To overcome this challenge, we use the historical local adapted model to restrict the direction of the inner loop and propose an elastic-constrained method. As a result, the current round inner loop keeps historical goals and adapts to better solutions. Experiments show our method boosts meta-learning convergence and improves personalization without additional calculation and communication. Our method achieved SOTA on all metrics in three public datasets.
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