Learning Linear Dynamical Systems via Spectral Filtering

Part of Advances in Neural Information Processing Systems 30 (NIPS 2017)

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Authors

Elad Hazan, Karan Singh, Cyril Zhang

Abstract

<p>We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for convexity of the loss functions. From this arises a polynomial-time algorithm with a near-optimal regret guarantee, with an analogous sample complexity bound for agnostic learning. Our algorithm is based on a novel filtering technique, which may be of independent interest: we convolve the time series with the eigenvectors of a certain Hankel matrix.</p>