  We provide theoretical investigation of curriculum learning in the context of
stochastic gradient descent when optimizing the convex linear regression loss.
We prove that the rate of convergence of an ideal curriculum learning method is
monotonically increasing with the difficulty of the examples. Moreover, among
all equally difficult points, convergence is faster when using points which
incur higher loss with respect to the current hypothesis. We then analyze
curriculum learning in the context of training a CNN. We describe a method
which infers the curriculum by way of transfer learning from another network,
pre-trained on a different task. While this approach can only approximate the
ideal curriculum, we observe empirically similar behavior to the one predicted
by the theory, namely, a significant boost in convergence speed at the
beginning of training. When the task is made more difficult, improvement in
generalization performance is also observed. Finally, curriculum learning
exhibits robustness against unfavorable conditions such as excessive
regularization.
