In many real-world situations a decision maker may make decisions across many separate reinforcement learning tasks in parallel, yet there has been very little work on concurrent RL. Building on the efficient exploration RL literature, we introduce two new concurrent RL algorithms and bound their sample complexity. We show that under some mild conditions, both when the agent is known to be acting in many copies of the same MDP, and when they are not the same but are taken from a finite set, we can gain linear improvements in the sample complexity over not sharing information. This is quite exciting as a linear speedup is the most one might hope to gain. Our preliminary experiments confirm this result and show empirical benefits.