mlsanityData to 7 Oct 2026

On Safety in Safe Bayesian Optimization

arXiv 2403.12948 ↗First posted 19 Mar 2024cs.LG stat.MLcited by 15

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Abstract (arXiv)

Optimizing an unknown function under safety constraints is a central task in robotics, biomedical engineering, and many other disciplines, and increasingly safe Bayesian Optimization (BO) is used for this. Due to the safety critical nature of these applications, it is of utmost importance that theoretical safety guarantees for these algorithms translate into the real world. In this work, we investigate three safety-related issues of the popular class of SafeOpt-type algorithms. First, these algorithms critically rely on frequentist uncertainty bounds for Gaussian Process (GP) regression, but concrete implementations typically utilize heuristics that invalidate all safety guarantees. We provide a detailed analysis of this problem and introduce Real-beta-SafeOpt, a variant of the SafeOpt algorithm that leverages recent GP bounds and thus retains all theoretical guarantees. Second, we identify assuming an upper bound on the reproducing kernel Hilbert space (RKHS) norm of the target function, a key technical assumption in SafeOpt-like algorithms, as a central obstacle to real-world usage. To overcome this challenge, we introduce the Lipschitz-only Safe Bayesian Optimization (LoSBO) algorithm, which guarantees safety without an assumption on the RKHS bound, and empirically show that this algorithm is not only safe, but also exhibits superior performance compared to the state-of-the-art on several function classes. Third, SafeOpt and derived algorithms rely on a discrete search space, making them difficult to apply to higher-dimensional problems. To widen the applicability of these algorithms, we introduce Lipschitz-only GP-UCB (LoS-GP-UCB), a variant of LoSBO applicable to moderately high-dimensional problems, while retaining safety.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 33 of its 74 references that are in the map. First posted on arXiv 19 Mar 2024.

Builds on

33 of 74 references.

References · 33

  1. 2019Introduction to Multi-Armed Banditscited by 475
  2. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 337
  3. 2016Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Roboticscited by 134
  4. 2018Learning-based Model Predictive Control for Safe Explorationcited by 116
  5. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  6. 2019Linear Stochastic Bandits Under Safety Constraintscited by 90
  7. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
  8. 2015Safe Controller Optimization for Quadrotors with Gaussian Processescited by 77
  9. 2019Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspacescited by 73
  10. 2016Safe Exploration in Finite Markov Decision Processes with Gaussian Processescited by 72
  11. 2019Uniform Error Bounds for Gaussian Process Regression with Application to Safe Controlcited by 64
  12. 2013Bandits and Experts in Metric Spacescited by 63
21 more
  1. 2016Conservative Banditscited by 58
  2. 2021Misspecified Gaussian Process Bandit Optimizationcited by 52
  3. 2015A General Framework for Constrained Bayesian Optimization using Information-based Searchcited by 50
  4. 2019No-Regret Bayesian Optimization with Unknown Hyperparameterscited by 50
  5. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  6. 2017Global optimization of Lipschitz functionscited by 39
  7. 2020Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothnesscited by 29
  8. 2021GoSafe: Globally Optimal Safe Robot Learningcited by 27
  9. 2023On the Sublinear Regret of GP-UCBcited by 25
  10. 2022GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systemscited by 17
  11. 2021Safe Learning and Optimization Techniques: Towards a Survey of the State of the Artcited by 16
  12. 2022Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posedcited by 16
  13. 2020Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functionscited by 15
  14. 2020Robot Learning with Crash Constraintscited by 15
  15. 2020Cautious Bayesian Optimization for Efficient and Scalable Policy Searchcited by 12
  16. 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
  17. 2018Provably Robust Learning-Based Approach for High-Accuracy Tracking Control of Lagrangian Systemscited by 9
  18. 2016Lazily Adapted Constant Kinky Inference for Nonparametric Regression and Model-Reference Adaptive Controlcited by 5
  19. 2023Lipschitz and H"older Continuity in Reproducing Kernel Hilbert Spacescited by 3
  20. 2019Safe global optimization of expensive noisy black-box functions in the δ-Lipschitz frameworkcited by 2
  21. 2023On kernel-based statistical learning in the mean field limitcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 5; 2026: 5.

15 papers.

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  1. 2024ActSafe: Active Exploration with Safety Constraints for Reinforcement Learningcited by 22
  2. 2025Safe exploration in reproducing kernel Hilbert spacescited by 10
  3. 2024PACSBO: Probably approximately correct safe Bayesian optimizationcited by 8
  4. 2024Towards safe Bayesian optimization with Wiener kernel regressioncited by 4
  5. 2025Optimal kernel regression bounds under energy-bounded noisecited by 4
  6. 2024Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processescited by 1
  7. 2025An Analysis of Safety Guarantees in Multi-Task Bayesian Optimizationcited by 1
  8. 2025Safe and Near-Optimal Control with Online Dynamics Learningcited by 1
  9. 2026Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual functioncited by 1
  10. 2026Safe learning-based control via function-based uncertainty quantificationcited by 1
  11. 2024Safe Bayesian Optimization for Complex Control Systems via Additive Gaussian Processescited by 0
  12. 2025Kernel conditional tests from learning-theoretic boundscited by 0
3 more
  1. 2026On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noisecited by 0
  2. 2026A Human-in-the-Loop Bayesian Optimization Framework for Constraint-Aware Bioprocess Developmentcited by 0
  3. 2026Computationally efficient safe exploration in reinforcement learningcited by 0