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Logarithmic Regret for Online Control

Author(s): Agarwal, Naman; Hazan, Elad; Singh, Karan

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Abstract: We study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics. This includes several well studied and influential frameworks such as the Kalman filter and the linear quadratic regulator. State of the art methods achieve regret which scales as T^0.5, where T is the time horizon. We show that the optimal regret in this fundamental setting can be significantly smaller, scaling as polylog(T). This regret bound is achieved by two different efficient iterative methods, online gradient descent and online natural gradient.
Publication Date: 2019
Citation: Agarwal, Naman, Elad Hazan, and Karan Singh. "Logarithmic Regret for Online Control." Advances in Neural Information Processing Systems 32 (2019).
ISSN: 1049-5258
Type of Material: Conference Article
Journal/Proceeding Title: Advances in Neural Information Processing Systems
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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