Autonomous robots in the real world should avert collisions with pedestrians and react quickly to sudden changes in the environment. Most local planners rely on static environment maps that cannot capture such critical elements of uncertainty. Learning based methods for end-to-end navigation have become popular recently, but it is still unclear how to incorporate collision avoidance in a simple, safe and quick manner. We propose a reinforcement learning curriculum based on domain randomization to train a high performing policy entirely in simulation. The policy is first trained in a simple obstacle-free environment to quickly learn point to point navigation. The learned policy is transferred to a dynamic environment to learn collision avoidance. The key idea is to randomize the obstacle dynamics to obtain a robust planner that can be directly deployed to the real world. The resultant policy outperforms conventional planners in dynamic real world environments, even when the robot is intentionally obstructed. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020.