Generalization error bounds for two-layer neural networks with Lipschitz loss function

We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its associated empirical measure, together with moment bounds for the associated stochastic gradient method. In the case of independent test data, we obtain a dimension-free rate of order O(n-1/2 ) on the n-sample generalization error, whereas without independence assumption, we derive a bound of order O(n^-1 / ( drm in+drm out ) ), where drm in, drm out denote input and output dimensions. Our bounds and their coefficients can be explicitly computed prior to the training of the model, and are confirmed by numerical simulations.