AC4MPC: Actor-Critic Reinforcement Learning for Nonlinear Model Predictive Control

\Ac{MPC} and \ac{RL} are two powerful control strategies with, arguably, complementary advantages. In this work, we show how actor-critic \ac{RL} techniques can be leveraged to improve the performance of \ac{MPC}. The \ac{RL} critic is used as an approximation of the optimal value function, and an actor roll-out provides an initial guess for primal variables of the \ac{MPC}. A parallel control architecture is proposed where each \ac{MPC} instance is solved twice for different initial guesses. Besides the actor roll-out initialization, a shifted initialization from the previous solution is used. Thereafter, the actor and the critic are again used to approximately evaluate the infinite horizon cost of these trajectories. The control actions from the lowest-cost trajectory are applied to the system at each time step. We establish that the proposed algorithm is guaranteed to outperform the original \ac{RL} policy plus an error term that depends on the accuracy of the critic and decays with the horizon length of the \ac{MPC} formulation. Moreover, we do not require globally optimal solutions for these guarantees to hold. The approach is demonstrated on an illustrative toy example and an \ac{AD} overtaking scenario.

Imitation Learning from Nonlinear MPC via the Exact Q-Loss and its Gauss-Newton Approximation

This work presents a novel loss function for learning nonlinear Model Predictive Control policies via Imitation Learning. Standard approaches to Imitation Learning neglect information about the expert and generally adopt a loss function based on the distance between expert and learned controls. In this work, we present a loss based on the Q-function directly embedding the performance objectives and constraint satisfaction of the associated Optimal Control Problem (OCP). However, training a Neural Network with the Q-loss requires solving the associated OCP for each new sample. To alleviate the computational burden, we derive a second Q-loss based on the Gauss-Newton approximation of the OCP resulting in a faster training time. We validate our losses against Behavioral Cloning, the standard approach to Imitation Learning, on the control of a nonlinear system with constraints. The final results show that the Q-function-based losses significantly reduce the amount of constraint violations while achieving comparable or better closed-loop costs.