We propose to train neural networks (NNs) using a novel variant of the ``Additively Preconditioned Trust-region Strategy'' (APTS). The proposed method is based on a parallelizable additive domain decomposition approach applied to the neural network's parameters. Built upon the TR framework, the APTS method ensures global convergence towards a minimizer. Moreover, it eliminates the need for computationally expensive hyper-parameter tuning, as the TR algorithm automatically determines the step size in each iteration. We demonstrate the capabilities, strengths, and limitations of the proposed APTS training method by performing a series of numerical experiments. The presented numerical study includes a comparison with widely used training methods such as SGD, Adam, LBFGS, and the standard TR method.
@article{arxiv.2312.13677,
title = {Parallel Trust-Region Approaches in Neural Network Training: Beyond Traditional Methods},
author = {Ken Trotti and Samuel A. Cruz Alegría and Alena Kopaničáková and Rolf Krause},
journal= {arXiv preprint arXiv:2312.13677},
year = {2023}
}