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In this paper, we are interested in optimal control problems with purelyeconomic costs, which often yield optimal policies having a (nearly) bang-bangstructure. We focus on policy approximations based on Model Predictive Control(MPC) and the use of the deterministic policy gradient method to optimize theMPC closed-loop performance in the presence of unmodelled stochasticity ormodel error. When the policy has a (nearly) bang-bang structure, we observethat the policy gradient method can struggle to produce meaningful steps in thepolicy parameters. To tackle this issue, we propose a homotopy strategy basedon the interior-point method, providing a relaxation of the policy during thelearning. We investigate a specific well-known battery storage problem, andshow that the proposed method delivers a homogeneous and faster learning than aclassical policy gradient approach.

MPC-based Reinforcement Learning for Economic Problems with Application to Battery Storage