We study the reinforcement learning problem in the setting of finite-horizon1episodic 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^2 SAT}) 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].