MPC-based Reinforcement Learning for Economic Problems with Application to Battery Storage
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In this paper, we are interested in optimal control problems with purely economic costs, which often yield optimal policies having a (nearly) bang-bang structure. We focus on policy approximations based on Model Predictive Control (MPC) and the use of the deterministic policy gradient method to optimize the MPC closed-loop performance in the presence of unmodelled stochasticity or model error. When the policy has a (nearly) bang-bang structure, we observe that the policy gradient method can struggle to produce meaningful steps in the policy parameters. To tackle this issue, we propose a homotopy strategy based on the interior-point method, providing a relaxation of the policy during the learning. We investigate a specific well-known battery storage problem, and show that the proposed method delivers a homogeneous and faster learning than a classical policy gradient approach.
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