Learning Linear Dynamical Systems via Spectral Filtering

Elad Hazan; Karan Singh; Cyril Zhang

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arXiv · 1711.00946

Learning Linear Dynamical Systems via Spectral Filtering

Elad Hazan·Karan Singh·Cyril Zhang

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Abstract

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.

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Elad Hazan, Karan Singh, Cyril Zhang. 2017-11-02. Learning Linear Dynamical Systems via Spectral Filtering. https://arxiv.org/abs/1711.00946

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