Gradient Descent Learns Linear Dynamical Systems
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
Text
Hardt et al. "Gradient Descent Learns Linear Dynamical Systems." Journal of Machine Learning Research, 2018.Markdown
[Hardt et al. "Gradient Descent Learns Linear Dynamical Systems." Journal of Machine Learning Research, 2018.](https://mlanthology.org/jmlr/2018/hardt2018jmlr-gradient/)BibTeX
@article{hardt2018jmlr-gradient,
title = {{Gradient Descent Learns Linear Dynamical Systems}},
author = {Hardt, Moritz and Ma, Tengyu and Recht, Benjamin},
journal = {Journal of Machine Learning Research},
year = {2018},
pages = {1-44},
volume = {19},
url = {https://mlanthology.org/jmlr/2018/hardt2018jmlr-gradient/}
}