  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.
