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arXiv · 2106.15775

Koopman Spectrum Nonlinear Regulators and Efficient Online Learning

Motoya Ohnishi·Isao Ishikawa·Kendall Lowrey·Masahiro Ikeda·Sham Kakade·Yoshinobu Kawahara
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Abstract

Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack predictability. In this work, we present a novel paradigm of controlling nonlinear systems via the minimization of the Koopman spectrum cost: a cost over the Koopman operator of the controlled dynamics. This induces a broader class of dynamical behaviors that evolve over stable manifolds such as nonlinear oscillators, closed loops, and smooth movements. We demonstrate that some dynamics characterizations that are not possible with a cumulative cost are feasible in this paradigm, which generalizes the classical eigenstructure and pole assignments to nonlinear decision making. Moreover, we present a sample efficient online learning algorithm for our problem that enjoys a sub-linear regret bound under some structural assumptions.

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Motoya Ohnishi, Isao Ishikawa, Kendall Lowrey, Masahiro Ikeda, Sham Kakade, Yoshinobu Kawahara. 2021-06-30. Koopman Spectrum Nonlinear Regulators and Efficient Online Learning. https://arxiv.org/abs/2106.15775

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