We address the decision-making capability within an end-to-end planning framework that focuses on motion prediction, decision-making, and trajectory planning. Specifically, we formulate decision-making and trajectory planning as a differentiable nonlinear optimization problem, which ensures compatibility with learning-based modules to establish an end-to-end trainable architecture. This optimization introduces explicit objectives related to safety, traveling efficiency, and riding comfort, guiding the learning process in our proposed pipeline. Intrinsic constraints resulting from the decision-making task are integrated into the optimization formulation and preserved throughout the learning process. By integrating the differentiable optimizer with a neural network predictor, the proposed framework is end-to-end trainable, aligning various driving tasks with ultimate performance goals defined by the optimization objectives. The proposed framework is trained and validated using the Waymo Open Motion dataset. The open-loop testing reveals that while the planning outcomes using our method do not always resemble the expert trajectory, they consistently outperform baseline approaches with improved safety, traveling efficiency, and riding comfort. The closed-loop testing further demonstrates the effectiveness of optimizing decisions and improving driving performance. Ablation studies demonstrate that the initialization provided by the learning-based prediction module is essential for the convergence of the optimizer as well as the overall driving performance.

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