Bridging RL and MPC for mixed-integer optimal control with application to Formula 1 race strategies

Abstract

We propose a hybrid reinforcement learning (RL) and model predictive control (MPC) framework for mixed-integer optimal control, where discrete variables enter the cost and dynamics but not the constraints. Existing hierarchical approaches learn a policy only for the discrete action space, leaving continuous optimization to MPC. Unlike these methods, we train an RL agent on the full hybrid action space, such that the learned critic approximates the Q-function of the underlying Markov decision process. During deployment, the RL actor is rolled out over the prediction horizon to parametrize an integer-free nonlinear MPC through the discrete action sequence and provide a continuous warm-start. The learned critic can additionally serve as a terminal cost to capture long-term performance. We prove recursive feasibility, and validate the framework on a Formula 1 race strategy problem, where an ablation study identifies the contribution of each learned component. The hybrid method achieves near-optimal performance relative to an offline mixed-integer nonlinear program benchmark, outperforming a standalone RL agent. Moreover, the hybrid scheme enables adaptation to unseen disturbances through modular MPC extensions at zero retraining cost.