Gradient Descent Learns Linear Dynamical Systems
This provides the first polynomial guarantees for linear systems identification, addressing a long-standing challenge in control theory and machine learning.
The authors tackled the problem of learning unknown linear time-invariant dynamical systems from noisy observations, proving that stochastic gradient descent efficiently converges to the global optimizer with polynomial running time and sample complexity bounds under strong assumptions.
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.