Before revision:  Typically, gradient descent-based methods are applied to minimize the expectation. This papershows that gradient descent can identify a global minimizer of the optimization problem with a well-controlled generalization error in the case of two-layer neural networks in the over-parameterization regime (i. e., the network width is sufficiently large).
After revision:  In this paper, we show that the gradient descent method can identify a global minimizer of the optimization problem with a well-controlled generalization error in the case of two-layer neural networks in the over-parameterization regime (i. e., the network width is sufficiently large).