# Falsification of Learning-Based Controllers through Multi-Fidelity Bayesian Optimization

arXiv: https://arxiv.org/abs/2212.14118 · HTML: https://mlsanity.com/paper/2212.14118/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 28 Dec 2022.

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian Optimization](https://mlsanity.com/paper/1703.01250/) (2017)
- [Safe Learning and Optimization Techniques: Towards a Survey of the State of the Art](https://mlsanity.com/paper/2101.09505/) (2021)
- [Verifying Controllers Against Adversarial Examples with Bayesian Optimization](https://mlsanity.com/paper/1802.08678/) (2018)
- [Finding Failures in High-Fidelity Simulation using Adaptive Stress Testing and the Backward Algorithm](https://mlsanity.com/paper/2107.12940/) (2021)
- [Waypoint Optimization Using Bayesian Optimization: A Case Study in Airborne Wind Energy Systems](https://mlsanity.com/paper/1910.12901/) (2019)
- [A Verification Framework for Certifying Learning-Based Safety-Critical Aviation Systems](https://mlsanity.com/paper/2205.04590/) (2022)
- [Economically Efficient Combined Plant and Controller Design Using Batch Bayesian Optimization: Mathematical Framework and Airborne Wind Energy Case Study](https://mlsanity.com/paper/1901.07521/) (2019)

## Built on by (most cited first, 4 of 4)

- [Optimizing Falsification for Learning-Based Control Systems: A Multi-Fidelity Bayesian Approach](https://mlsanity.com/paper/2409.08097/) (2024)
- [Towards provable probabilistic safety for scalable embodied AI systems](https://mlsanity.com/paper/2506.05171/) (2025)
- [Falsification-driven reinforcement learning for maritime motion planning](https://mlsanity.com/paper/2510.06970/) (2025)
- [Can We Formally Verify Neural PDE Surrogates? SMT Compilation of Small Fourier Neural Operators](https://mlsanity.com/paper/2605.08938/) (2026)

## Abstract (arXiv)

Simulation-based falsification is a practical testing method to increase confidence that the system will meet safety requirements. Because full-fidelity simulations can be computationally demanding, we investigate the use of simulators with different levels of fidelity. As a first step, we express the overall safety specification in terms of environmental parameters and structure this safety specification as an optimization problem. We propose a multi-fidelity falsification framework using Bayesian optimization, which is able to determine at which level of fidelity we should conduct a safety evaluation in addition to finding possible instances from the environment that cause the system to fail. This method allows us to automatically switch between inexpensive, inaccurate information from a low-fidelity simulator and expensive, accurate information from a high-fidelity simulator in a cost-effective way. Our experiments on various environments in simulation demonstrate that multi-fidelity Bayesian optimization has falsification performance comparable to single-fidelity Bayesian optimization but with much lower cost.