Data-Parallel Neural Network Training via Nonlinearly Preconditioned Trust-Region Method
Samuel A. Cruz Alegría, Ken Trotti, Alena Kopaničáková, Rolf Krause
TL;DR
This work addresses the challenge of scalable neural network training without heavy hyperparameter tuning by introducing a data-parallel Additively Preconditioned Trust Region (APTS) method. APTS leverages a right-preconditioned additive domain-decomposition framework, combining parallel local TR steps with a global TR update, and uses a Lanczos-style L-SR1 Hessian approximation to enable indefinite curvature handling. The approach achieves competitive validation accuracy to Adam on MNIST and CIFAR-10 without tuning, while reducing synchronization costs compared to standard data-parallel SGD/Adam; however, performance can degrade as the number of subdomains grows due to gradient-approximation variance. Overall, APTS offers a hyperparameter-free, globally convergent alternative for parallel NN training with practical implications for reducing tuning effort and communication overhead in large-scale settings.
Abstract
Parallel training methods are increasingly relevant in machine learning (ML) due to the continuing growth in model and dataset sizes. We propose a variant of the Additively Preconditioned Trust-Region Strategy (APTS) for training deep neural networks (DNNs). The proposed APTS method utilizes a data-parallel approach to construct a nonlinear preconditioner employed in the nonlinear optimization strategy. In contrast to the common employment of Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), which are both variants of gradient descent (GD) algorithms, the APTS method implicitly adjusts the step sizes in each iteration, thereby removing the need for costly hyperparameter tuning. We demonstrate the performance of the proposed APTS variant using the MNIST and CIFAR-10 datasets. The results obtained indicate that the APTS variant proposed here achieves comparable validation accuracy to SGD and Adam, all while allowing for parallel training and obviating the need for expensive hyperparameter tuning.