# Safe Real-Time Optimization using Multi-Fidelity Gaussian Processes

arXiv: https://arxiv.org/abs/2111.05589 · HTML: https://mlsanity.com/paper/2111.05589/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 10 Nov 2021.

## Builds on (most cited first, 8 of 8)

- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Reinforcement Learning for Batch Bioprocess Optimization](https://mlsanity.com/paper/1904.07292/) (2019)
- [Stochastic data-driven model predictive control using Gaussian processes](https://mlsanity.com/paper/1908.01786/) (2019)
- [Chance Constrained Policy Optimization for Process Control and Optimization](https://mlsanity.com/paper/2008.00030/) (2020)
- [Identification and online updating of dynamic models for demand response of an industrial air separation unit](https://mlsanity.com/paper/2009.13999/) (2020)
- [Convergence Certificate for Stochastic Derivative-Free Trust-Region Methods based on Gaussian Processes](https://mlsanity.com/paper/2010.01120/) (2020)

## Built on by (most cited first, 5 of 5)

- [Machine learning for industrial sensing and control: A survey and practical perspective](https://mlsanity.com/paper/2401.13836/) (2024)
- [Deep Gaussian Process-based Multi-fidelity Bayesian Optimization for Simulated Chemical Reactors](https://mlsanity.com/paper/2210.17213/) (2022)
- [Safe and Adaptive Decision-Making for Optimization of Safety-Critical Systems: The ARTEO Algorithm](https://mlsanity.com/paper/2211.05495/) (2022)
- [A Guide to Bayesian Optimization in Bioprocess Engineering](https://mlsanity.com/paper/2508.10642/) (2025)
- [A Human-in-the-Loop Bayesian Optimization Framework for Constraint-Aware Bioprocess Development](https://mlsanity.com/paper/2606.19230/) (2026)

## Abstract (arXiv)

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.