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Safety and efficiency are two key elements for planning and control in autonomous driving. Theoretically, model-based optimization methods, such as Model Predictive Control (MPC), can provide such optimal driving policies. Their computational complexity, however, grows exponentially with horizon length and number of surrounding vehicles. This makes them impractical for real-time implementation, particularly when nonlinear models are considered. To enable a fast and approximately optimal driving policy, we propose a safe imitation framework, which contains two hierarchical layers. The first layer, defined as the policy layer, is represented by a neural network that imitates a long-term expert driving policy via imitation learning. The second layer, called the execution layer, is a short-term model-based optimal controller that tracks and further fine-tunes the reference trajectories proposed by the policy layer with …