optimal learning rate
There are many variations of stochastic gradient descent: Adam, RMSProp, Adagrad, etc. All of them let you set the learning rate. This parameter tells the optimizer how far to move the weights in the direction opposite of the gradient for a mini-batch.
Leslie N. Smith describes a powerful technique to select a range of learning rates for a neural network in section 3.3 of the 2015 paper “Cyclical Learning Rates for Training Neural Networks”
The training should start from a relatively large learning rate because, in the beginning, random weights are far from optimal, and then the learning rate can decrease during training to allow more fine-grained weight updates.
The trick is to train a network starting from a low learning rate and increase the learning rate exponentially for every batch. Just run the training multiple times, one mini-batch at a time. Increase the learning rate after each mini-batch by multiplying it by a small constant. Stop the procedure when the loss gets a lot higher than the previously observed best value (e.g., when current loss > best loss * 4).