Year: 2019
Type: preprint
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 fundamental frameworks such as the Kalman filter and the linear quadratic regulator. State of the art methods achieve regret which scales as $O(\sqrt{T})$, where $T$ is the time horizon. We show that the optimal regret in this setting can be significantly smaller, scaling as $O(\text{poly}(\log T))$. This regret bound is achieved by two different efficient iterative methods, online gradient descent and online natural gradient.
Source: arXiv (Cornell University)
Authors: Agarwal, Naman, Hazan, Elad, Singh, Karan
Institutions: Alphabet (United States), Princeton University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2970857099