[HTML][HTML] Error bounds for kernel-based approximations of the Koopman operator
We consider the data-driven approximation of the Koopman operator for stochastic
differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the …
differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the …
Learning invariant representations of time-homogeneous stochastic dynamical systems
We consider the general class of time-homogeneous stochastic dynamical systems, both
discrete and continuous, and study the problem of learning a representation of the state that …
discrete and continuous, and study the problem of learning a representation of the state that …
Error analysis of kernel EDMD for prediction and control in the Koopman framework
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to
approximate the Koopman operator for deterministic and stochastic (control) systems. This …
approximate the Koopman operator for deterministic and stochastic (control) systems. This …
Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces
I Ishikawa, Y Hashimoto, M Ikeda… - arXiv preprint arXiv …, 2024 - arxiv.org
This paper presents a novel approach for estimating the Koopman operator defined on a
reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method …
reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method …
Nonparametric Control-Koopman Operator Learning: Flexible and Scalable Models for Prediction and Control
Linearity of Koopman operators and simplicity of their estimators coupled with model-
reduction capabilities has lead to their great popularity in applications for learning dynamical …
reduction capabilities has lead to their great popularity in applications for learning dynamical …
Extended Dynamic Mode Decomposition: Sharp bounds on the sample efficiency
We rigorously derive novel and sharp finite-data error bounds for highly sample-efficient
Extended Dynamic Mode Decomposition (EDMD) for both iid and ergodic sampling. In …
Extended Dynamic Mode Decomposition (EDMD) for both iid and ergodic sampling. In …
[PDF][PDF] Consistent Long-Term Forecasting of Ergodic Dynamical Systems
We study the problem of forecasting the evolution of a function of the state (observable) of a
discrete ergodic dynamical system over multiple time steps. The elegant theory of Koopman …
discrete ergodic dynamical system over multiple time steps. The elegant theory of Koopman …
Data-driven optimal feedback laws via kernel mean embeddings
This paper proposes a fully data-driven approach for optimal control of nonlinear control-
affine systems represented by a stochastic diffusion. The focus is on the scenario where both …
affine systems represented by a stochastic diffusion. The focus is on the scenario where both …
Consistent long-term forecasting of ergodic dynamical systems
We study the evolution of distributions under the action of an ergodic dynamical system,
which may be stochastic in nature. By employing tools from Koopman and transfer operator …
which may be stochastic in nature. By employing tools from Koopman and transfer operator …
Operator World Models for Reinforcement Learning
Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for
sequential decision-making. However, it is not directly applicable to Reinforcement Learning …
sequential decision-making. However, it is not directly applicable to Reinforcement Learning …