We have developed a reinforcement learning method for training a real-time control policy of electric grid systems under uncertain contingency events. In particular, we use graph convolutional neural networks (GCNs) that directly encode the physical power system topology and predict the power system resilience (i.e., total load lost between initial contingency and full recovery) for a given initial contingency event. We have prototyped the proposed method and plan to scale up on the testbed machine.