mlsanityData to 7 Oct 2026

Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces

arXiv 1902.03229 ↗First posted 8 Feb 2019cs.LG stat.MLcited by 73

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Abstract (arXiv)

Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm (LineBO) that restricts the problem to a sequence of iteratively chosen one-dimensional sub-problems that can be solved efficiently. We show that our algorithm converges globally and obtains a fast local rate when the function is strongly convex. Further, if the objective has an invariant subspace, our method automatically adapts to the effective dimension without changing the algorithm. When combined with the SafeOpt algorithm to solve the sub-problems, we obtain the first safe Bayesian optimization algorithm with theoretical guarantees applicable in high-dimensional settings. We evaluate our method on multiple synthetic benchmarks, where we obtain competitive performance. Further, we deploy our algorithm to optimize the beam intensity of the Swiss Free Electron Laser with up to 40 parameters while satisfying safe operation constraints.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Feb 2019.

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Citing papers per year: 2021: 12; 2022: 15; 2023: 9; 2024: 15; 2025: 13; 2026: 9.

73 papers.

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  1. 2021High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspacescited by 139
  2. 2021Multi-Objective Bayesian Optimization over High-Dimensional Search Spacescited by 87
  3. 2024Vanilla Bayesian Optimization Performs Great in High Dimensionscited by 87
  4. 2023Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?cited by 35
  5. 2023Bayesian Optimization over High-Dimensional Combinatorial Spaces via Dictionary-based Embeddingscited by 24
  6. 2021Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processescited by 23
  7. 2024A survey and benchmark of high-dimensional Bayesian optimization of discrete sequencescited by 22
  8. 2024ActSafe: Active Exploration with Safety Constraints for Reinforcement Learningcited by 22
  9. 2022Active Exploration via Experiment Design in Markov Chainscited by 19
  10. 2021Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applicationscited by 17
  11. 2021Risk-averse Heteroscedastic Bayesian Optimizationcited by 17
  12. 2022GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systemscited by 17
38 more
  1. 2022Policy-Based Bayesian Experimental Design for Non-Differentiable Implicit Modelscited by 15
  2. 2024On Safety in Safe Bayesian Optimizationcited by 15
  3. 2025Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spacescited by 13
  4. 2021Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selectioncited by 12
  5. 2021Bias-Robust Bayesian Optimization via Dueling Banditscited by 11
  6. 2022Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learningcited by 11
  7. 2022Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practicecited by 11
  8. 2022Scalable First-Order Bayesian Optimization via Structured Automatic Differentiationcited by 10
  9. 2022Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spacescited by 9
  10. 2022Information-Theoretic Safe Exploration with Gaussian Processescited by 9
  11. 2024Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimizationcited by 9
  12. 2025We Still Don't Understand High-Dimensional Bayesian Optimizationcited by 9
  13. 2023Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimizationcited by 8
  14. 2023Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimationcited by 8
  15. 2024Safe Guaranteed Exploration for Non-linear Systemscited by 8
  16. 2021Stochastic Gradient Line Bayesian Optimization for Efficient Noise-Robust Optimization of Parameterized Quantum Circuitscited by 7
  17. 2022Tuning Particle Accelerators with Safety Constraints using Bayesian Optimizationcited by 7
  18. 2021Global optimization using random embeddingscited by 6
  19. 2022Graph Machine Learning for Design of High-Octane Fuelscited by 6
  20. 2023Constrained Causal Bayesian Optimizationcited by 6
  21. 2024Boundary Exploration for Bayesian Optimization With Unknown Physical Constraintscited by 6
  22. 2024This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimizationcited by 6
  23. 2025Thompson Sampling via Fine-Tuning of LLMscited by 6
  24. 2026Safe Exploration via Policy Priorscited by 6
  25. 2022Adjusted Expected Improvement for Cumulative Regret Minimization in Noisy Bayesian Optimizationcited by 5
  26. 2022MARS: Meta-Learning as Score Matching in the Function Spacecited by 5
  27. 2023Unleashing the Potential of Acquisition Functions in High-Dimensional Bayesian Optimizationcited by 5
  28. 2023Towards Safe Multi-Task Bayesian Optimizationcited by 5
  29. 2024Principled Bayesian Optimisation in Collaboration with Human Expertscited by 5
  30. 2026BayeSQP: Bayesian Optimization through Sequential Quadratic Programmingcited by 5
  31. 2026Conformal Policy Controlcited by 5
  32. 2022Optimization on Manifolds via Graph Gaussian Processescited by 4
  33. 2024Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systemscited by 4
  34. 2023A Bayesian Optimization approach for calibrating large-scale activity-based transport modelscited by 3
  35. 2025Amortized Safe Active Learning for Real-Time Data Acquisition: Pretrained Neural Policies From Simulated Nonparametric Functionscited by 3
  36. 2024Expected Coordinate Improvement for High-Dimensional Bayesian Optimizationcited by 2
  37. 2024High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspacescited by 2
  38. 2025Safety and optimality in learning-based control at low computational costcited by 2

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