Approximate model predictive control (AMPC) has emerged as an approach to tackle the computational burden of MPC, aiming to approximate the MPC policy with a computationally cheaper surrogate, such as neural networks. So far, the standard approach to obtaining such a surrogate policy has been based on naive behavioral cloning. This approach, however, has significant drawbacks, resulting in the surrogate policy potentially failing to provide the original MPC guarantees. To tackle this, a tailored AMPC imitation learning (IL) procedure was developed recently, enabling consistent learning of a surrogate policy and ensuring that the learned policy maintains the original MPC safety and stability guarantees. This development allows for MPC-based control functions in safety-critical industrial settings. The goal of your thesis is to extend the statistical properties of the proposed IL procedure by analyzing the rate at which the learned policy converges to the MPC policy, ultimately aiming to provide sample bounds on the error between the policies. Moreover, the thesis could cover the investigation of more general error estimations, stopping criteria, and studies on sample efficiency. Last but not least, the thesis will also focus on the deployment of the developed AMPC IL procedure to a real-world automated driving problem, including a comparison with other existing approaches.