  Adaptively controlling and minimizing regret in unknown dynamical systems
while controlling the growth of the system state is crucial in real-world
applications. In this work, we study the problem of stabilization and regret
minimization of linear over-actuated dynamical systems. We propose an
optimism-based algorithm that leverages possibility of switching between
actuating modes in order to alleviate state explosion during initial time
steps. We theoretically study the rate at which our algorithm learns a
stabilizing controller and prove that it achieves a regret upper bound of
$\mathcal{O}(\sqrt{T})$.
