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.

翻译：联邦学习是一种多方协作训练机器学习模型的方法，但禁止各方共享数据。联邦学习面临的挑战之一是客户端之间的数据非独立同分布（non-IID），因为单一模型无法拟合所有客户端的数据分布。为此，引入元学习（如Per-FedAvg）以应对该挑战。元学习为所有客户端学习共享的初始参数，每个客户端通过梯度下降将初始化参数快速适配至本地数据分布，从而实现模型个性化。然而，由于非凸损失函数和采样更新的随机性，元学习方法在同客户端的本地适配中存在不稳定的目标。这种不同适配方向的波动阻碍了元学习的收敛。为克服这一挑战，我们利用历史本地适配模型来约束内循环方向，提出一种弹性约束方法。由此，当前轮次的内循环保留历史目标并适配至更优解。实验表明，该方法在不增加计算和通信成本的前提下提升了元学习的收敛速度与个性化性能。在三个公开数据集上，我们的方法在所有指标上均达到最优水平（SOTA）。