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Differential Equation Based Framework for Deep Reinforcement Learning

: Gottschalk, Simon

Fulltext urn:nbn:de:0011-n-6249618 (4.5 MByte PDF)
MD5 Fingerprint: 3333d0a2ec0100d03ce3fa47fa7cd5f0
Created on: 24.2.2021

Stuttgart: Fraunhofer Verlag, 2021, 130 pp.
Zugl.: Kaiserslautern, TU, Diss., 2020
ISBN: 978-3-8396-1682-6
Dissertation, Electronic Publication
Fraunhofer ITWM ()
neural networks & fuzzy systems; machine learning; probability & statistics; Deep Reinforcement Learning; optimal control; necessary optimality conditions; machine learning; applied mathematics; optimization; Mathematiker; Informatiker; Data Scientists

In this thesis, we contribute to new directions within Reinforcement Learning, which are important for many practical applications such as the control of biomechanical models. We deepen the mathematical foundations of Reinforcement Learning by deriving theoretical results inspired by classical optimal control theory. In our derivations, Deep Reinforcement Learning serves as our starting point. Based on its working principle, we derive a new type of Reinforcement Learning framework by replacing the neural network by a suitable ordinary differential equation. Coming up with profound mathematical results within this differential equation based framework turns out to be a challenging research task, which we address in this thesis. Especially the derivation of optimality conditions takes a central role in our investigation. We establish new optimality conditions tailored to our specific situation and analyze a resulting gradient based approach. Finally, we illustrate the power, working principle and versatility of this approach by performing control tasks in the context of a navigation in the two dimensional plane, robot motions, and actuations of a human arm model.