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

Understand

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques and proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes.

• The provided theoretical analysis in terms of cumulative regret focuses on previously stated sufficient conditions of the resulting `Cautious Bayesian MPC' algorithm and shows Lipschitz continuity of the future reward function in the case of linear MPC problems.
• In the case of nonlinear MPC problems, it is shown that commonly required assumptions for nonlinear MPC optimization techniques provide sufficient criteria for model-based RL using posterior sampling.
• Furthermore, it is shown that the proposed constraint tightening implies a bound on the expected number of unsafe learning episodes in the linear and nonlinear case using a soft-constrained MPC formulation.