Fed-LAMB: Layer-wise and Dimension-wise Locally Adaptive Federated Learning

In the emerging paradigm of Federated Learning (FL), large amount of clients such as mobile devices are used to train possibly high-dimensional models on their respective data. Combining (dimension-wise) adaptive gradient methods (e.g., Adam, AMSGrad) with FL has been an active direction, which is shown to outperform traditional SGD based FL in many cases. In this paper, we focus on the problem of training federated deep neural networks, and propose a novel FL framework which further introduces layer-wise adaptivity to the local model updates to accelerate the convergence of adaptive FL methods. Our framework includes two variants based on two recent locally adaptive federated learning algorithms. Theoretically, we provide a convergence analysis of our layer-wise FL methods, coined Fed-LAMB and Mime-LAMB, which match the convergence rate of state-of-the-art results in adaptive FL and exhibits linear speedup in terms of the number of workers. Experimental results on various datasets and models, under both IID and non-IID local data settings, show that both Fed-LAMB and Mime-LAMB achieve faster convergence speed and better generalization performance, compared to various recent adaptive FL methods.