Reviews: Learning Linear Dynamical Systems via Spectral Filtering

Linear dynamical systems are a mainstay of control theory. This led to the breakthrough work many decades ago of Kalman filters, without which the moon landing would have been impossible. This paper explores the problem of online learning (in the regret model) of dynamical systems, and improves upon previous work in this setting that was restricted to the single input single output (SISO) case [HMR 16]. Unlike that paper, the present work shows that regret bounded learning of an LDS is possible without making assumptions on the spectral structure (polynomially bounded eigengap), and signal source limitations. The key new idea is a convex relation of the original non-convex problem, which as the paper shows, is "the central driver" of their approach.