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.

翻译：我们提出使用一种新颖的"加性预处理信任域策略"（APTS）变体来训练神经网络（NNs）。该方法基于对神经网络参数采用可并行的加性区域分解策略。在信任域（TR）框架基础上，APTS方法能够保证全局收敛到极小值点。此外，该方法无需进行计算成本高昂的超参数调优，因为信任域算法可在每次迭代中自动确定步长。通过一系列数值实验，我们展示了所提出的APTS训练方法的能力、优势与局限性。本数值研究包括与SGD、Adam、LBFGS及标准信任域方法等广泛使用训练方法的对比。