Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations
(PDEs) associated to them have been widely used in models from engineering, finance, and …

We consider stochastic optimization when one only has access to biased stochastic oracles
of the objective, and obtaining stochastic gradients with low biases comes at high costs. This …

Deep learning algorithms have been applied very successfully in recent years to a range of
problems out of reach for classical solution paradigms. Nevertheless, there is no completely …

In this article, we consider convergence of stochastic gradient descent schemes (SGD)
under weak assumptions on the underlying landscape. More explicitly, we show that on the …

Gradient descent (GD) type optimization methods are the standard instrument to train
artificial neural networks (ANNs) with recti_ed linear unit (ReLU) activation. Despite the …

Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of
machine learning applications. In this article we perform a rigorous strong error analysis for …

In this article we investigate blow up phenomena for gradient descent optimization methods
in the training of artificial neural networks (ANNs). Our theoretical analysis is focused on …

In this article we study the stochastic gradient descent (SGD) optimization method in the
training of fully connected feedforward artificial neural networks with ReLU activation. The …

We consider stochastic optimization when one only has access to biased stochastic oracles
of the objective and the gradient, and obtaining stochastic gradients with low biases comes …

In many numerical simulations stochastic gradient descent (SGD) type optimization methods
perform very effectively in the training of deep neural networks (DNNs) but till this day it …