Corpus ID: 232290401

Towards a Dimension-Free Understanding of Adaptive Linear Control

  title={Towards a Dimension-Free Understanding of Adaptive Linear Control},
  author={Juan C. Perdomo and Max Simchowitz and Alekh Agarwal and Peter L. Bartlett},
We study the problem of adaptive control of the linear quadratic regulator for systems in very high, or even infinite dimension. We demonstrate that while sublinear regret requires finite dimensional inputs, the ambient state dimension of the system need not be bounded in order to perform online control. We provide the first regret bounds for LQR which hold for infinite dimensional systems, replacing dependence on ambient dimension with more natural notions of problem complexity. Our guarantees… Expand