Learning from Dynamics
summary
Given one long input-output trajectory, the paper proves polynomial-time parameter recovery for linear dynamical systems under marginal stability plus bounded condition numbers of the observability and controllability matrices, using a method of moments to estimate Markov parameters and the classical Ho–Kalman reconstruction. Key technical trick is constructing finite-variance estimators by canceling long-range dependencies via coefficients tied to the system’s characteristic polynomial (Cayley–Hamilton) and finding them via a convex program.
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chapters (8)
- 0:00Workshop introduction
- 3:02Linear dynamical systems
- 10:59Learning LDS challenges
- 16:02Strict stability problems
- 23:54New algorithm philosophy
- 27:09Estimating Markov parameters
- 39:29Summary and future
- 40:12Question and answer session
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