  We propose a novel training method based on nonlinear multilevel minimization
techniques, commonly used for solving discretized large scale partial
differential equations. Our multilevel training method constructs a multilevel
hierarchy by reducing the number of samples. The training of the original model
is then enhanced by internally training surrogate models constructed with fewer
samples. We construct the surrogate models using first-order consistency
approach. This gives rise to surrogate models, whose gradients are stochastic
estimators of the full gradient, but with reduced variance compared to standard
stochastic gradient estimators. We illustrate the convergence behavior of the
proposed multilevel method to machine learning applications based on logistic
regression. A comparison with subsampled Newton's and variance reduction
methods demonstrate the efficiency of our multilevel method.

Machine Learning;Machine Learning