  Bayesian optimization has become a powerful tool for safe online optimization
of systems, due to its high sample efficiency and noise robustness. For further
speed-up reduced physical models of the system can be incorporated into the
optimization to accelerate the process, since the models are able to offer an
approximation of the actual system, and sampling from them is significantly
cheaper. The similarity between model and reality is represented by additional
hyperparameters and learned within the optimization process. Safety is an
important criteria for online optimization methods like Bayesian optimization,
which has been addressed by recent literature, which provide safety guarantees
under the assumption of known hyperparameters. However, in practice this is not
applicable. Therefore, we extend the robust Gaussian process uniform error
bounds to meet the multi-task setting, which involves the calculation of a
confidence region from the hyperparameter posterior distribution utilizing
Markov chain Monte Carlo methods. Then, using the robust safety bounds,
Bayesian optimization is applied to safely optimize the system while
incorporating measurements of the models. Simulations show that the
optimization can be significantly accelerated compared to other
state-of-the-art safe Bayesian optimization methods depending on the fidelity
of the models.

Machine Learning;Systems and Control;Systems and Control;Machine Learning