# Safe Bayesian optimization across noise models via scenario programming

arXiv: https://arxiv.org/abs/2512.11580 · HTML: https://mlsanity.com/paper/2512.11580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Almost Optimal Algorithms for Linear Stochastic Bandits with Heavy-Tailed Payoffs](https://mlsanity.com/paper/1810.10895/) (2018)
- [Bayesian Optimization under Heavy-tailed Payoffs](https://mlsanity.com/paper/1909.07040/) (2019)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Safe exploration in reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2503.10352/) (2025)
- [PACSBO: Probably approximately correct safe Bayesian optimization](https://mlsanity.com/paper/2409.01163/) (2024)
- [Improved Regret Bounds for Linear Bandits with Heavy-Tailed Rewards](https://mlsanity.com/paper/2506.04775/) (2025)

## Built on by (most cited first, 1 of 1)

- [Safe learning-based control via function-based uncertainty quantification](https://mlsanity.com/paper/2604.01173/) (2026)

## Abstract (arXiv)

Safe Bayesian optimization (BO) with Gaussian processes is an effective tool for tuning control policies in safety-critical real-world systems, specifically due to its sample efficiency and safety guarantees. However, most safe BO algorithms assume homoscedastic sub-Gaussian measurement noise, an assumption that does not hold in many relevant applications. In this article, we propose a straightforward yet rigorous approach for safe BO across noise models, including homoscedastic sub-Gaussian and heteroscedastic heavy-tailed distributions. We provide a high-probability bound on the measurement noise via the scenario approach, integrate these bounds into high probability confidence intervals, and prove safety and optimality for our proposed safe BO algorithm. We deploy our algorithm in synthetic examples and in tuning a controller for the Franka Emika manipulator in simulation.