Dynamics of Learning and Learning of Dynamics
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Date
2021
Publication Type
Doctoral Thesis
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Abstract
This dissertation investigates the reciprocal benefits between machine learning and dynamical systems with the focus on generative models from machine learning and the Lyapunov theory of stability from dynamical systems. In the first direction, the established theory of control and dynamical systems is used to study the dynamic behavior of learning algorithms. In the other direction, the machine learning toolbox is used to approach problems in system identification and control theory in a data-centric way.
It is often the case in machine learning that the problem is formulated as the minimization of a cost function. However, it turned out, in particular in generative models, that formulating the problem as a game whose equilibrium corresponds to the desired solution could lead to much better performance. This~\emph{gamification} of learning algorithms has encouraged studying the properties of the desired equilibrium to get insight into the learning process when idealized as a dynamical system. We take this approach to study a generic class of generative models where multiple players are trained with coupled dynamics.
In control, when the physical equations of the system are not known in advance, which is most often the case in practice, the standard first step is to identify the system from its observed trajectories, and then design a controller to drive the system towards an equilibrium with the desired properties. Even though this process is fairly standard for linear systems, it quickly becomes intractable for nonlinear systems. It is shown in this dissertation that combining learning algorithms with established concepts such as~\emph{Lyapunov function} from nonlinear dynamical systems can facilitate both identification and control synthesis. A trainable Lyapunov function is a key component in these algorithms that is co-trained with the vector field of the system for the identification task, and with the controller for the control synthesis task.
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Examiner : Schölkopf, Bernhard
Examiner : Rätsch, Gunnar
Examiner : Krause, Andreas
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ETH Zurich
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Subject
Machine Learning; Dynamical Systems; Generative Adversarial Networks (GAN); Energy-based models; Kernel methods; Lyapunov Function; CONTROL SYSTEMS THEORY (MATHEMATICS); SYSTEM IDENTIFICATION (CONTROL SYSTEMS THEORY)
Organisational unit
09664 - Schölkopf, Bernhard / Schölkopf, Bernhard