Safe Bayesian optimization across noise models via scenario programming

2025-12-12

AI Summary

Existing safe Bayesian optimization (SBO) methods are constrained by the homoscedastic sub-Gaussian noise assumption, limiting robustness in real-world safety-critical applications with heterogeneous or heavy-tailed noise. Method: We propose a noise-model-agnostic safe optimization framework, the first to integrate scenario optimization into SBO. It synergistically combines Gaussian process regression, adaptive confidence interval construction, and a robust upper-confidence-bound (UCB) strategy to uniformly handle both homoscedastic and heteroscedastic, as well as light- and heavy-tailed noise. Contribution/Results: Our framework provides rigorous high-probability safety guarantees and asymptotic optimality. Experiments on synthetic benchmarks and real-world Franka Emika robotic controller tuning demonstrate efficient convergence with zero safety violations, significantly enhancing robustness and practicality for safety-critical systems under heterogeneous heavy-tailed noise.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Addresses safe Bayesian optimization under diverse noise models
• Ensures safety and optimality in control policy tuning
• Applies scenario programming for robust noise estimation

Innovation

• Scenario programming for noise modeling
• High-probability bounds via scenario approach
• Safe BO across heteroscedastic heavy-tailed noise