The goal of hyperparameter tuning is to reach the point where test loss is horizontal on the graph over model complexity.
Underfitting can be observed with a small learning rate, simple architecture, or complex data distribution. You can observe underfitting decrease by seeing more drastic results at the outset, followed by a more horizontal line further into training. You can use the LR range test to find a good learning rate range, and then use a cyclical learning rate to move up and down within that range.
The LR range test is a run of training that starts at a small learning rate and then slowly increases until the rate is too high and the validation loss increases. This article talks a little about what performing the LR range test looks like in practice. (They don’t go into great technical detail unfortunately.) This PyTorch implementation of LRRT looks good.
Regularization should be balanced with the dataset and architecture. It’s silly to have a small learning rate with lots of regularization, when you could have a large learning rate and less regularization (accomplishing the same regularizing effect with faster convergence). The solution is to perform the LR range test under a variety of regularization conditions in order to find an optimal balance.
In their study of batch size, they took into account the total execution time for training. Modelers are interested in reaching optimal test performance in the minimum amount of wall time. A larger batch size allows for higher learning rate (#regularization) and thus faster convergence, but the benefit tapers off, probably because of the reduction in number of iterations.
Momentum and learning rate are interconnected; changing one changes the optimal value for the other. It turns out that using cyclical momentum that decreases as LR increases reaches similar results to a best constant momentum, but allows for larger learning rates.
For weight decay, the best value should remain constant through training. Validation loss early in training is sufficient for determining a good value. Smaller datasets and architectures seem to require larger values for weight decay.
There’s a nice recipe in section 5 for putting all of this together.
The fast.ai paper uses a variant of the 1cycle learning policy with warm-up and annealing on both the learning rate and momentum.