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.

SOFIM: Stochastic Optimization Using Regularized Fisher Information Matrix

This paper introduces a new stochastic optimization method based on the regularized Fisher information matrix (FIM), named SOFIM, which can efficiently utilize the FIM to approximate the Hessian matrix for finding Newton's gradient update in large-scale stochastic optimization of machine learning models. It can be viewed as a variant of natural gradient descent (NGD), where the challenge of storing and calculating the full FIM is addressed through making use of the regularized FIM and directly finding the gradient update direction via Sherman-Morrison matrix inversion. Additionally, like the popular Adam method, SOFIM uses the first moment of the gradient to address the issue of non-stationary objectives across mini-batches due to heterogeneous data. The utilization of the regularized FIM and Sherman-Morrison matrix inversion leads to the improved convergence rate with the same space and time complexities as stochastic gradient descent (SGD) with momentum. The extensive experiments on training deep learning models on several benchmark image classification datasets demonstrate that the proposed SOFIM outperforms SGD with momentum and several state-of-the-art Newton optimization methods, such as Nystrom-SGD, L-BFGS, and AdaHessian, in term of the convergence speed for achieving the pre-specified objectives of training and test losses as well as test accuracy.