  Mini-batch sub-sampling (MBSS) is favored in deep neural network training to
reduce the computational cost. Still, it introduces an inherent sampling error,
making the selection of appropriate learning rates challenging. The sampling
errors can manifest either as a bias or variances in a line search. Dynamic
MBSS re-samples a mini-batch at every function evaluation. Hence, dynamic MBSS
results in point-wise discontinuous loss functions with smaller bias but larger
variance than static sampled loss functions. However, dynamic MBSS has the
advantage of having larger data throughput during training but requires the
complexity regarding discontinuities to be resolved. This study extends the
gradient-only surrogate (GOS), a line search method using quadratic
approximation models built with only directional derivative information, for
dynamic MBSS loss functions. We propose a gradient-only approximation line
search (GOALS) with strong convergence characteristics with defined optimality
criterion. We investigate GOALS's performance by applying it on various
optimizers that include SGD, RMSprop and Adam on ResNet-18 and EfficientNetB0.
We also compare GOALS's against the other existing learning rate methods. We
quantify both the best performing and most robust algorithms. For the latter,
we introduce a relative robust criterion that allows us to quantify the
difference between an algorithm and the best performing algorithm for a given
problem. The results show that training a model with the recommended learning
rate for a class of search directions helps to reduce the model errors in
multimodal cases.
