  There has been a recent surge of interest in understanding the convergence of
gradient descent (GD) and stochastic gradient descent (SGD) in
overparameterized neural networks. Most previous works assume that the training
data is provided a priori in a batch, while less attention has been paid to the
important setting where the training data arrives in a stream. In this paper,
we study the streaming data setup and show that with overparamterization and
random initialization, the prediction error of two-layer neural networks under
one-pass SGD converges in expectation. The convergence rate depends on the
eigen-decomposition of the integral operator associated with the so-called
neural tangent kernel (NTK). A key step of our analysis is to show a random
kernel function converges to the NTK with high probability using the VC
dimension and McDiarmid's inequality.
