  We study the reinforcement learning problem in the setting of finite-horizon
episodic Markov Decision Processes (MDPs) with $S$ states, $A$ actions, and
episode length $H$. We propose a model-free algorithm UCB-Advantage and prove
that it achieves $\tilde{O}(\sqrt{H^2SAT})$ regret where $T = KH$ and $K$ is
the number of episodes to play. Our regret bound improves upon the results of
[Jin et al., 2018] and matches the best known model-based algorithms as well as
the information theoretic lower bound up to logarithmic factors. We also show
that UCB-Advantage achieves low local switching cost and applies to concurrent
reinforcement learning, improving upon the recent results of [Bai et al.,
2019].
