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.

翻译：贝叶斯优化凭借其高样本效率和噪声鲁棒性，已成为系统安全在线优化的强大工具。为进一步加速优化过程，可将系统的简化物理模型纳入优化框架——这些模型能提供实际系统的近似，且从中采样的成本显著更低。模型与真实系统之间的相似性通过额外超参数表示，并在优化过程中进行学习。安全性是贝叶斯优化等在线优化方法的重要准则，最新文献在已知超参数假设下提供了相关安全性保证，但该假设在实际中并不适用。为此，我们将鲁棒高斯过程均匀误差界扩展以适应多任务场景，该扩展利用马尔可夫链蒙特卡洛方法从超参数后验分布中计算置信区域。随后，基于鲁棒安全界，在融合模型测量值的同时，应用贝叶斯优化实现系统的安全优化。仿真结果表明，与当前最先进的安全贝叶斯优化方法相比，本方法可依据模型保真度显著加速优化进程。