Cautious Bayesian MPC: Regret Analysis and Bounds on the Number of Unsafe Learning Episodes

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes. The provided theoretical analysis in terms cumulative regret focuses on previously stated sufficient conditions resulting ‘Cautious Bayesian MPC’ algorithm shows Lipschitz continuity future reward function case linear MPC problems. In nonlinear problems, it is shown that commonly required assumptions for optimization provide criteria model-based RL using sampling. Furthermore, proposed implies bound expected number unsafe episodes soft-constrained formulation. efficiency method illustrated numerical examples.