%0 Journal Article %1 hazan2019nonstochastic %A Hazan, Elad %A Kakade, Sham M. %A Singh, Karan %D 2019 %K non-linear optimization %T The Nonstochastic Control Problem %U http://arxiv.org/abs/1911.12178 %X 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 T^2/3, in this setting.

@article{hazan2019nonstochastic, abstract = {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 T^{2/3}, in this setting.}, added-at = {2020-01-22T18:00:55.000+0100}, author = {Hazan, Elad and Kakade, Sham M. and Singh, Karan}, biburl = {https://www.bibsonomy.org/bibtex/243056b5210fed6c61220e6d39853c20d/kirk86}, description = {[1911.12178] The Nonstochastic Control Problem}, interhash = {19d60a58f61c130f65ff3581db494abc}, intrahash = {43056b5210fed6c61220e6d39853c20d}, keywords = {non-linear optimization}, note = {cite arxiv:1911.12178Comment: To appear at Algorithmic Learning Theory (ALT) 2020; small revisions from the last ver}, timestamp = {2020-01-22T18:00:55.000+0100}, title = {The Nonstochastic Control Problem}, url = {http://arxiv.org/abs/1911.12178}, year = 2019 }