  In this work, we study model-based reinforcement learning (RL) in unknown
stabilizable linear dynamical systems. When learning a dynamical system, one
needs to stabilize the unknown dynamics in order to avoid system blow-ups. We
propose an algorithm that certifies fast stabilization of the underlying system
by effectively exploring the environment with an improved exploration strategy.
We show that the proposed algorithm attains $\tilde{\mathcal{O}}(\sqrt{T})$
regret after $T$ time steps of agent-environment interaction. We also show that
the regret of the proposed algorithm has only a polynomial dependence in the
problem dimensions, which gives an exponential improvement over the prior
methods. Our improved exploration method is simple, yet efficient, and it
combines a sophisticated exploration policy in RL with an isotropic exploration
strategy to achieve fast stabilization and improved regret. We empirically
demonstrate that the proposed algorithm outperforms other popular methods in
several adaptive control tasks.
