FAGH: Accelerating Federated Learning with Approximated Global Hessian

In federated learning (FL), the significant communication overhead due to the slow convergence speed of training the global model poses a great challenge. Specifically, a large number of communication rounds are required to achieve the convergence in FL. One potential solution is to employ the Newton-based optimization method for training, known for its quadratic convergence rate. However, the existing Newton-based FL training methods suffer from either memory inefficiency or high computational costs for local clients or the server. To address this issue, we propose an FL with approximated global Hessian (FAGH) method to accelerate FL training. FAGH leverages the first moment of the approximated global Hessian and the first moment of the global gradient to train the global model. By harnessing the approximated global Hessian curvature, FAGH accelerates the convergence of global model training, leading to the reduced number of communication rounds and thus the shortened training time. Experimental results verify FAGH's effectiveness in decreasing the number of communication rounds and the time required to achieve the pre-specified objectives of the global model performance in terms of training and test losses as well as test accuracy. Notably, FAGH outperforms several state-of-the-art FL training methods.