Riccati updates for online linear quadratic control

We study an online setting of the linear quadratic Gaussian optimal control problem on a sequence of cost functions, where similar to classical online optimization, the future decisions are made by only knowing the cost in hindsight. We introduce a modified online Riccati update that under some boundedness assumptions, leads to logarithmic regret bounds, improving the best known square-root bound. In particular, for the scalar case we achieve the logarithmic regret without any boundedness assumption. As opposed to earlier work, proposed method does not rely on solving semi-definite programs at each stage.