# Bayesian Optimization applied for accelerated Virtual Validation of the Autonomous Driving Function

arXiv: https://arxiv.org/abs/2507.22769 · HTML: https://mlsanity.com/paper/2507.22769/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Adversarial scenarios and safety testing, one of 9 directions in End-to-end autonomous driving.
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 30 Jul 2025.

## Placed in

- End-to-end autonomous driving / [Adversarial scenarios and safety testing](https://mlsanity.com/driving/adversarial-scenarios-and-safety-testing/)

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

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Waymax: An Accelerated, Data-Driven Simulator for Large-Scale Autonomous Driving Research](https://mlsanity.com/paper/2310.08710/) (2023)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Criticality Metrics for Automated Driving: A Review and Suitability Analysis of the State of the Art](https://mlsanity.com/paper/2108.02403/) (2021)
- [A Survey on Scenario-Based Testing for Automated Driving Systems in High-Fidelity Simulation](https://mlsanity.com/paper/2112.00964/) (2021)
- [Safety-Critical Scenario Generation Via Reinforcement Learning Based Editing](https://mlsanity.com/paper/2306.14131/) (2023)
- [A Scenario-Based Platform for Testing Autonomous Vehicle Behavior Prediction Models in Simulation](https://mlsanity.com/paper/2110.14870/) (2021)
- [Fast integrators with sensitivity propagation for use in CasADi](https://mlsanity.com/paper/2211.01982/) (2022)
- [On the Need for a Statistical Foundation in Scenario-Based Testing of Autonomous Vehicles](https://mlsanity.com/paper/2505.02274/) (2025)
- [Correlation of Software-in-the-Loop Simulation with Physical Testing for Autonomous Driving](https://mlsanity.com/paper/2406.03040/) (2024)
- [Reinforcement Learning for Testing Interdependent Requirements in Autonomous Vehicles: An Empirical Study](https://mlsanity.com/paper/2502.15792/) (2025)
- [An Application of Scenario Exploration to Find New Scenarios for the Development and Testing of Automated Driving Systems in Urban Scenarios](https://mlsanity.com/paper/2205.08202/) (2022)
- [DynNPC: Finding More Violations Induced by ADS in Simulation Testing through Dynamic NPC Behavior Generation](https://mlsanity.com/paper/2411.19567/) (2024)

## Abstract (arXiv)

Rigorous Verification and Validation (V&V) of Autonomous Driving Functions (ADFs) is paramount for ensuring the safety and public acceptance of Autonomous Vehicles (AVs). Current validation relies heavily on simulation to achieve sufficient test coverage within the Operational Design Domain (ODD) of a vehicle, but exhaustively exploring the vast parameter space of possible scenarios is computationally expensive and time-consuming. This work introduces a framework based on Bayesian Optimization (BO) to accelerate the discovery of critical scenarios. We demonstrate the effectiveness of the framework on an Model Predictive Controller (MPC)-based motion planner, showing that it identifies hazardous situations, such as off-road events, using orders of magnitude fewer simulations than brute-force Design of Experiments (DoE) methods. Furthermore, this study investigates the scalability of the framework in higher-dimensional parameter spaces and its ability to identify multiple, distinct critical regions within the ODD of the motion planner used as the case study .