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Applying reinforcement learning to autonomous driving entails particular challenges, primarily due to dynamically changing traffic flows. To address such challenges, it is necessary to quickly determine response strategies to the changing intentions of surrounding vehicles. This paper proposes a new policy optimization method for safe driving using graph-based interaction-aware constraints. In this framework, the motion prediction and control modules are trained simultaneously while sharing a latent representation that contains a social context. To reflect social interactions, we illustrate the movements of agents in graph form and filter the features with the graph convolution networks. This helps preserve the spatiotemporal locality of adjacent nodes. Furthermore, we create feedback loops to combine these two modules effectively. As a result, this approach encourages the learned controller to be safe from dynamic risks and renders the motion prediction robust to abnormal movements. In the experiment, we set up a navigation scenario comprising various situations with CARLA, an urban driving simulator. The experiments show state-of-the-art performance on navigation strategy and motion prediction compared to the baselines.