Lars Grüne (University of Bayreuth)

Titel: Can neural networks solve high dimensional optimal feedback control problems?
Abstract: Deep Reinforcement Learning has established itself as a standard method for solving nonlinear optimal feedback control problems. In this method, the optimal value function (and in some variants also the optimal feedback law) is stored using a deep neural network. Hence, the applicability of this approach to high-dimensional problems crucially relies on the network's ability to store a high-dimensional function. It is known that for general high-dimensional functions, neural networks suffer from the same exponential growth of the number of coefficients as traditional grid based methods, the so-called curse of dimensionality. In this talk, we use methods from distributed optimal control to describe optimal control problems in which this problem does not occur.