TY - JOUR
T1 - The Nonstochastic Control Problem
AU - Hazan, Elad
AU - Kakade, Sham M.
AU - Singh, Karan
N1 - Funding Information:
We thank Naman Agarwal, Max Simchowitz and Cyril Zhang for helpful discussions. Sham Kakade acknowledges funding from the Washington Research Foundation for Innovation in Data-intensive Discovery and the ONR award N00014-18-1-2247. Karan Singh gratefully acknowledges support from the Porter Ogden Jacobus Fellowship.
Publisher Copyright:
© 2020 E. Hazan, S.M. Kakade & K. Singh.
PY - 2020
Y1 - 2020
N2 - We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an optimal controller here is hindered by the latter’s dependence on the yet unknown perturbations and costs. Instead, we measure regret against an optimal linear policy in hindsight, and give the first efficient algorithm that guarantees a sublinear regret bound, scaling as O(T2/3), in this setting.
AB - We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions. In contrast to classical control, the a priori determination of an optimal controller here is hindered by the latter’s dependence on the yet unknown perturbations and costs. Instead, we measure regret against an optimal linear policy in hindsight, and give the first efficient algorithm that guarantees a sublinear regret bound, scaling as O(T2/3), in this setting.
KW - Control Theory
KW - Online Learning
KW - Robust Control
KW - System Identification
UR - http://www.scopus.com/inward/record.url?scp=85161366562&partnerID=8YFLogxK
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M3 - Conference article
AN - SCOPUS:85161366562
SN - 2640-3498
VL - 117
SP - 408
EP - 421
JO - Proceedings of Machine Learning Research
JF - Proceedings of Machine Learning Research
T2 - 31st International Conference on Algorithmic Learning Theory, ALT 2020
Y2 - 8 February 2020 through 11 February 2020
ER -