Bayesian optimization has emerged as a highly effective tool for the safe online optimization of systems, due to its high sample efficiency and noise robustness. To further enhance its efficiency, reduced physical models of the system can be incorporated into the optimization process, accelerating it. These models are able to offer an approximation of the actual system, and evaluating them is significantly cheaper. The similarity between the model and reality is represented by additional hyperparameters, which are learned within the optimization process. Safety is a crucial criterion for online optimization methods such as Bayesian optimization, which has been addressed by recent works that provide safety guarantees under the assumption of known hyperparameters. In practice, however, this does not apply. 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. Subsequently, the robust safety bounds are employed to facilitate the safe optimization of the system, while incorporating measurements of the models. Simulation results indicate that the optimization can be significantly accelerated for expensive to evaluate functions in comparison to other state-of-the-art safe Bayesian optimization methods, contingent on the fidelity of the models.

翻译：贝叶斯优化因其高样本效率与噪声鲁棒性，已成为系统安全在线优化的高效工具。为进一步提升效率，可将系统的简化物理模型融入优化过程以加速收敛。这类模型能够提供实际系统的近似表示，且其评估成本显著更低。模型与真实系统间的相似性由额外超参数表征，这些参数将在优化过程中学习得到。安全性是贝叶斯优化等在线优化方法的关键准则，近期研究已在超参数已知的假设下提供了安全保证。然而在实践中该假设往往不成立。为此，我们将鲁棒高斯过程均匀误差界扩展至多任务场景，通过马尔可夫链蒙特卡洛方法从超参数后验分布计算置信区域。随后，利用鲁棒安全边界在整合模型测量的同时实现系统安全优化。仿真结果表明，对于评估代价高昂的函数，相较于其他先进安全贝叶斯优化方法，本方法能显著加速优化进程，其效果取决于模型的保真度。