Safe Bayesian optimization across noise models via scenario programming

TL;DR

This paper introduces a robust safe Bayesian optimization method that accommodates various noise models, including heteroscedastic heavy-tailed distributions, ensuring safety and optimality in real-world control tuning.

Contribution

It extends safe Bayesian optimization to handle diverse noise models using scenario programming, providing safety guarantees under broader measurement noise conditions.

Findings

Successfully applied to synthetic examples

Tuned a controller for Franka Emika manipulator in simulation

Provided high-probability safety and optimality bounds

Abstract

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.