Gradient Descent Learns Linear Dynamical Systems
Machine Learning
2019-02-12 v2 Data Structures and Algorithms
Optimization and Control
Machine Learning
Abstract
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running time and sample complexity bounds under strong but natural assumptions. Linear systems identification has been studied for many decades, yet, to the best of our knowledge, these are the first polynomial guarantees for the problem we consider.
Cite
@article{arxiv.1609.05191,
title = {Gradient Descent Learns Linear Dynamical Systems},
author = {Moritz Hardt and Tengyu Ma and Benjamin Recht},
journal= {arXiv preprint arXiv:1609.05191},
year = {2019}
}
Comments
updated with more experimental results and references to prior work; published in JMLR 2018