Stable Anderson Acceleration for Deep Learning

TL;DR

This paper introduces a stabilized Anderson acceleration method combined with an adaptive moving average to improve convergence speed in deep learning training, especially under stochastic oscillations caused by mini-batch sampling.

Contribution

It proposes a novel combination of Anderson acceleration with an adaptive smoothing technique and an automatic criterion to enhance deep learning optimization stability.

Findings

Effective stabilization of Anderson acceleration in stochastic settings

Improved convergence in deep learning models across various tasks

Demonstrated scalability on high-performance computing systems

Abstract

Anderson acceleration (AA) is an extrapolation technique designed to speed-up fixed-point iterations like those arising from the iterative training of DL models. Training DL models requires large datasets processed in randomly sampled batches that tend to introduce in the fixed-point iteration stochastic oscillations of amplitude roughly inversely proportional to the size of the batch. These oscillations reduce and occasionally eliminate the positive effect of AA. To restore AA's advantage, we combine it with an adaptive moving average procedure that smoothes the oscillations and results in a more regular sequence of gradient descent updates. By monitoring the relative standard deviation between consecutive iterations, we also introduce a criterion to automatically assess whether the moving average is needed. We applied the method to the following DL instantiations: (i) multi-layer perceptrons (MLPs) trained on the open-source graduate admissions dataset for regression, (ii) physics informed neural networks (PINNs) trained on source data to solve 2d and 100d Burgers' partial differential equations (PDEs), and (iii) ResNet50 trained on the open-source ImageNet1k dataset for image classification. Numerical results obtained using up to 1,536 NVIDIA V100 GPUs on the OLCF supercomputer Summit showed the stabilizing effect of the moving average on AA for all the problems above.