Safe Real-Time Optimization using Multi-Fidelity Gaussian Processes
This addresses optimization for uncertain processes, such as in chemical engineering, but appears incremental as it combines existing methods.
The paper tackles real-time optimization under system-model mismatch by integrating derivative-free optimization and multi-fidelity Gaussian processes within a Bayesian framework, resulting in a practical approach demonstrated in numerical case studies like a photobioreactor optimization.
This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes within a Bayesian optimization framework. The proposed scheme uses two Gaussian processes for the stochastic system, one emulates the (known) process model, and another, the true system through measurements. In this way, low fidelity samples can be obtained via a model, while high fidelity samples are obtained through measurements of the system. This framework captures the system's behavior in a non-parametric fashion while driving exploration through acquisition functions. The benefit of using a Gaussian process to represent the system is the ability to perform uncertainty quantification in real-time and allow for chance constraints to be satisfied with high confidence. This results in a practical approach that is illustrated in numerical case studies, including a semi-batch photobioreactor optimization problem.