Geometry and Dynamical Systems in Machine Learning and Control

Citation

Dorobantu, Victor David (2023) Geometry and Dynamical Systems in Machine Learning and Control. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/x271-r088. https://resolver.caltech.edu/CaltechTHESIS:06012023-194820518

Abstract

For many problems of interest in machine learning and control, we have access to rich information about underlying geometry and dynamics; we can leverage this information to build robust and performant solutions in new algorithms, optimizations, and designs. In this thesis we study four problem settings to stress this central assumption. First, we study conformal generative modeling, using computational geometry techniques to simplify and register complex 2D surfaces and enabling the use of a variety of flow-based generative models as plug-and-play subroutines. Second, we study data-driven robust optimization problems in control, modeling the precise impact of dynamics uncertainty in several control frameworks using convex geometry. Third, we study compactly-restrictable policy optimization, constraining the available states and actions in reinforcement learning and optimal control problems to be consistent with the inherent dynamics of the systems to be controlled. Finally, we study nonlinear model predictive control on Lie groups as applied to a 3D hopping robot platform, developing a control methodology compatible with nontrivial state space geometry and hybrid system dynamics.

Thesis Files