A New Approach to Learning Linear Dynamical Systems

A New Approach to Learning Linear Dynamical Systems

Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic guarantees. Naturally, learning the dynamics of a linear dynamical sys...

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Hauptverfasser: Bakshi, Ainesh, Liu, Allen, Moitra, Ankur, Yau, Morris
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Computer Science - Data Structures and Algorithms
Computer Science - Learning
Mathematics - Optimization and Control
Statistics - Machine Learning
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creator Bakshi, Ainesh
Liu, Allen
Moitra, Ankur
Yau, Morris
description Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic guarantees. Naturally, learning the dynamics of a linear dynamical system from linear measurements has been intensively studied since Rudolph Kalman's pioneering work in the 1960's. Towards these ends, we provide the first polynomial time algorithm for learning a linear dynamical system from a polynomial length trajectory up to polynomial error in the system parameters under essentially minimal assumptions: observability, controllability, and marginal stability. Our algorithm is built on a method of moments estimator to directly estimate Markov parameters from which the dynamics can be extracted. Furthermore, we provide statistical lower bounds when our observability and controllability assumptions are violated.
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subjects Computer Science - Data Structures and Algorithms
Computer Science - Learning
Mathematics - Optimization and Control
Statistics - Machine Learning
title A New Approach to Learning Linear Dynamical Systems
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