  An online policy learning problem of linear control systems is studied. In
this problem, the control system is known and linear, and a sequence of
quadratic cost functions is revealed to the controller in hindsight, and the
controller updates its policy to achieve a sublinear regret, similar to online
optimization. A modified online Riccati algorithm is introduced that under some
boundedness assumption leads to logarithmic regret bound. In particular, the
logarithmic regret for the scalar case is achieved without boundedness
assumption. Our algorithm, while achieving a better regret bound, also has
reduced complexity compared to earlier algorithms which rely on solving
semi-definite programs at each stage.
