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Congrats to Johannes Müller on his dissertation and new role at RWTH Aachen

Published July 3, 2024

Congratulations to Johannes Christoph Müller. He completed his dissertation the geometric properties of specific optimization problems in reinforcement learning models. He now continues his scientific career as a member of the Information Processing group at RWTH Aachen.

 

Johannes’ research is driven by whether one can leverage the geometric properties of specific optimization problems to design more efficient algorithms for their solution. He focuses on challenges in reinforcement learning and numerical solvers for partial differential equations that utilize deep neural networks. Both are very vivid research areas where Reinforcement Learning played an essential role in developing large language models like ChatGPT. 

His dissertation at the University of Leipzig, titled “Geometry of Optimization in Markov Decision Processes and Neural Network Based PDE Solvers”, was supervised by his group leader Guido Montúfar and Nihat Ay.

Johannes describes his thesis as follows:
„Reinforcement learning models the interaction of an agent with its environment. In my thesis, I have demonstrated that if the agent has incomplete information about its environment, the problem becomes equivalent to the optimization of a linear function subject to polynomial constraints, where the degree of the polynomial depends on the type of observations available. At a high level, this describes the curvature of decision problems with incomplete state information, where problems with complete state information were known to be equivalent to a linear program and thus flat. I hope that such geometric insights can advance both the theoretical understanding and the development of practical algorithms for these problems. “

Before starting the PhD in Leipzig, Johannes studied Mathematics at the University of Freiburg and the University of Warwick and has now joined the group of Professor Semih Çaycı on the Mathematics of Information Processing at RWTH Aachen.