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

Logarithmic Regret in Adaptive Control of Noisy Linear Quadratic Regulator Systems Using Hints