Rollout Then Optimize: A One-Step Newton Refinement of Learned Policies for Nonlinear Model Predictive Control

We propose a computationally efficient rollout-then-optimize method to improve a learned control policy at deployment time. A learned policy provides a nominal trajectory, which is refined online by a single Newton step implemented via a Riccati recursion within a model predictive control (MPC) scheme. This refinement combines model knowledge with the learned policy at minimal additional computational cost. We establish bounds on the approximation error of the learned policy relative to the MPC policy and show that one Newton step reduces the suboptimality of the learned rollout quadratically in the policy approximation error. The proposed controller is validated in simulation on a constrained trajectory-tracking task for a quadcopter with nonlinear dynamics. Results highlight that the Newton step significantly improves the learned policy, achieving performance close to a fully converged MPC solution while requiring roughly half of the computational time. The code is available at https://github.com/aghezz1/rl-riccati.