  The problem of regret minimization for online adaptive control of
linear-quadratic systems is studied. In this problem, the true system
transition parameters (matrices $A$ and $B$) are unknown, and the objective is
to design and analyze algorithms that generate control policies with sublinear
regret. Recent studies show that when the system parameters are fully unknown,
there exists a choice of these parameters such that any algorithm that only
uses data from the past system trajectory at best achieves a square root of
time horizon regret bound, providing a hard fundamental limit on the achievable
regret in general. However, it is also known that (poly)-logarithmic regret is
achievable when only matrix $A$ or only matrix $B$ is unknown. We present a
result, encompassing both scenarios, showing that (poly)-logarithmic regret is
achievable when both of these matrices are unknown, but a hint is periodically
given to the controller.
