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Path planning for mobile robots in large dynamic environments is a challenging problem, as the robots are required to efficiently reach their given goals while simultaneously avoiding potential conflicts with other robots or dynamic objects. In the presence of dynamic obstacles, traditional solutions usually employ re-planning strategies, which re-call a planning algorithm to search for an alternative path whenever the robot encounters a conflict. However, such re-planning strategies often cause unnecessary detours. To address this issue, we propose a learning-based technique that exploits environmental spatio-temporal information. Different from existing learning-based methods, we introduce a globally guided reinforcement learning approach (G2RL), which incorporates a novel reward structure that generalizes to arbitrary environments. We apply G2RL to solve the multi-robot path planning problem in a fully distributed reactive manner. We evaluate our method across different map types, obstacle densities, and the number of robots. Experimental results show that G2RL generalizes well, outperforming existing distributed methods, and performing very similarly to fully centralized state-of-the-art benchmarks.