%0 Journal Article %1 lale2020regret %A Lale, Sahin %A Azizzadenesheli, Kamyar %A Hassibi, Babak %A Anandkumar, Anima %D 2020 %K bounds control optimization theory %T Regret Minimization in Partially Observable Linear Quadratic Control %U http://arxiv.org/abs/2002.00082 %X We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to design a controller. We propose a novel way to decompose the regret and provide an end-to-end sublinear regret upper bound for partially observable linear quadratic control. Finally, we provide stability guarantees and establish a regret upper bound of $\mathcalO(T^2/3)$ for ExpCommit, where $T$ is the time horizon of the problem.

@article{lale2020regret, abstract = {We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to design a controller. We propose a novel way to decompose the regret and provide an end-to-end sublinear regret upper bound for partially observable linear quadratic control. Finally, we provide stability guarantees and establish a regret upper bound of $\tilde{\mathcal{O}}(T^{2/3})$ for ExpCommit, where $T$ is the time horizon of the problem.}, added-at = {2020-05-22T03:38:51.000+0200}, author = {Lale, Sahin and Azizzadenesheli, Kamyar and Hassibi, Babak and Anandkumar, Anima}, biburl = {https://www.bibsonomy.org/bibtex/2b73740f1eb9af8f5b8d105117ac53b30/kirk86}, description = {[2002.00082] Regret Minimization in Partially Observable Linear Quadratic Control}, interhash = {8bc2b6f85ced1b4a41d46b398ddb344c}, intrahash = {b73740f1eb9af8f5b8d105117ac53b30}, keywords = {bounds control optimization theory}, note = {cite arxiv:2002.00082}, timestamp = {2020-05-22T03:38:51.000+0200}, title = {Regret Minimization in Partially Observable Linear Quadratic Control}, url = {http://arxiv.org/abs/2002.00082}, year = 2020 }