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.

我们提出了一种使用“加法预条件化信任域策略”（APTS）的新变体训练神经网络（NNs）的方法，该方法是基于可并行化的加法域分解方法应用于神经网络参数的。该方法构建在TR框架之上，确保全局收敛到最小化器，并且消除了计算成本昂贵的超参数调优的需求，因为TR算法会自动确定每次迭代的步长。通过进行一系列的数值实验证明了所提出的APTS训练方法的能力、优势和局限性。该数值研究包括与广泛使用的训练方法（如SGD、Adam、LBFGS和标准TR方法）的比较。

神经网络训练中的并行信任区域方法：超越传统方法