4 papers
Non-convergence to global minimizers for Adam and stochastic gradient descent optimization and constructions of local minimizers in the training of artificial neural networks
Arnulf Jentzen, Adrian Riekert
Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of arti…
Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems
Christian Beck, Arnulf Jentzen, Konrad Kleinberg +1
Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision maki…
The necessity of depth for artificial neural networks to approximate certain classes of smooth and bounded functions without the curse of dimensionality
Lukas Gonon, Robin Graeber, Arnulf Jentzen
In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In partic…
Normalized gradient flow optimization in the training of ReLU artificial neural networks
Simon Eberle, Arnulf Jentzen, Adrian Riekert +1
The training of artificial neural networks (ANNs) is nowadays a highly relevant algorithmic procedure with many applications in science and industry. Roughly speaking, ANNs can be…