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This paper investigates the combination of model predictive control (MPC)concepts and posterior sampling techniques and proposes a simple constrainttightening technique to introduce cautiousness during explorative learningepisodes. The provided theoretical analysis in terms of cumulative regretfocuses on previously stated sufficient conditions of the resulting `CautiousBayesian MPC' algorithm and shows Lipschitz continuity of the future rewardfunction in the case of linear MPC problems. In the case of nonlinear MPCproblems, it is shown that commonly required assumptions for nonlinear MPCoptimization techniques provide sufficient criteria for model-based RL usingposterior sampling. Furthermore, it is shown that the proposed constrainttightening implies a bound on the expected number of unsafe learning episodesin the linear and nonlinear case using a soft-constrained MPC formulation. Theefficiency of the method is illustrated using numerical examples.

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