Guiding End-to-End Driving Models with Endpoint-Constrained Trajectory Optimization

Abstract

End-to-end driving policies are commonly trained through open-loop behavior cloning, yet they must ultimately operate in closed-loop when deployed on a vehicle, creating a fundamental mismatch between training and execution. Beyond the commonly studied effects of covariate shift and causal confusion, we identify a complementary factor for this open-loop/closed-loop gap: waypoint-based supervision and displacement metrics do not ensure that the intermediate trajectory is physically coherent or easy for the controller to track. We observe that these inconsistencies concentrate primarily at intermediate waypoints, while the predicted endpoint remains comparatively reliable. Based on this observation, we introduce Endpoint-Constrained Optimization (ECO), a lightweight postprocessing layer that anchors the trajectory to the vehicle's executed history, preserves the policy's predicted endpoint, and reshapes the intermediate waypoints to improve feasibility. ECO requires no map, privileged simulator state, or additional training, and can be inserted between a broad range of waypoint-emitting policies and their controllers. Across two closed-loop simulators, it improves the aggregate closed-loop score of all six evaluated generative and regression-based driving policies, and the gains tend to increase with how often the base plans violate motion limits. On HUGSIM, ECO improves VaVAM from 18.1 to 31.0 HD-Score (+71%), achieving 1st place on the HUGSIM Closed-Loop Driving Challenge. Similarly, on AlpaSim, ECO increases the scene scores of VaVAM and DiffusionDrive by 123% and 22%, respectively. These results show that for a broad collection of end-to-end driving models, repairing the intermediate geometry of predicted trajectories without changing the policy's predicted endpoint can substantially improve closed-loop performance.