Can neural networks solve high dimensional optimal feedback control problems? (Prof. Lars Grüne, Applied Mathematics, University of Bayreuth)

Systems & Control Seminar

• Wednesday 12.06.2024, 16:00 
• Room A145, Building 3403, Appelstr. 11

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.
 

Biographical information

Lars Grüne has been Professor for Applied Mathematics at the University of Bayreuth, Germany, since 2002. He received his Diploma and Ph.D. in Mathematics in 1994 and 1996, respectively, from the University of Augsburg and his habilitation from the J.W. Goethe University in Frankfurt/M in 2001. He held or holds visiting positions at the Universities of Rome `Sapienza' (Italy), Padova (Italy), Melbourne (Australia), Paris IX - Dauphine (France), Newcastle (Australia) and IIT Bombay (India). Prof. Grüne was General Chair of the 25th International Symposium on Mathematical Theory on Networks and Systems (MTNS 2022), he is Editor-in-Chief of the journal Mathematics of Control, Signals and Systems (MCSS) and is or was Associate Editor of various other journals, including the Journal of Optimization Theory and Applications (JOTA), Mathematical Control and Related Fields (MCRF) and the IEEE Control Systems Letters (CSS-L). His research interests lie in the area of mathematical systems and control theory with a focus on numerical and optimization-based methods for nonlinear systems.