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A Tutorial on Bayesian Optimization

arXiv 1807.02811 ↗First posted 8 Jul 2018stat.ML cs.LG math.OCcited by 734

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Abstract (arXiv)

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

Key facts. Cited by 734 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jul 2018.

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Citing papers per year: 2021: 93; 2022: 109; 2023: 112; 2024: 131; 2025: 155; 2026: 134.

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  1. 2024Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Surveycited by 641
  2. 2021Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020cited by 146
  3. 2023Unexpected Improvements to Expected Improvement for Bayesian Optimizationcited by 144
  4. 2021High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspacescited by 139
  5. 2024Large Language Models to Enhance Bayesian Optimizationcited by 127
  6. 2022Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modelingcited by 126
  7. 2025Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systemscited by 125
  8. 2023Structured Pruning for Deep Convolutional Neural Networks: A surveycited by 122
  9. 2021Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvementcited by 115
  10. 2021DEUP: Direct Epistemic Uncertainty Predictioncited by 102
  11. 2022Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoderscited by 99
  12. 2021Multi-Objective Bayesian Optimization over High-Dimensional Search Spacescited by 87
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  1. 2022Recent Advances in Bayesian Optimizationcited by 74
  2. 2023PFNs4BO: In-Context Learning for Bayesian Optimizationcited by 70
  3. 2023InstructZero: Efficient Instruction Optimization for Black-Box Large Language Modelscited by 68
  4. 2023MLCopilot: Unleashing the Power of Large Language Models in Solving Machine Learning Taskscited by 66
  5. 2023Black Box Adversarial Prompting for Foundation Modelscited by 62
  6. 2021Exploration in Deep Reinforcement Learning: From Single-Agent to Multiagent Domaincited by 57
  7. 2025DeepScientist: Advancing Frontier-Pushing Scientific Findings Progressivelycited by 56
  8. 2021High-Dimensional Experimental Design and Kernel Banditscited by 55
  9. 2022Joint Entropy Search for Maximally-Informed Bayesian Optimizationcited by 55
  10. 2021High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learningcited by 54
  11. 2024Feedback Efficient Online Fine-Tuning of Diffusion Modelscited by 52
  12. 2021Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spacescited by 51
  13. 2022Pareto Set Learning for Expensive Multi-Objective Optimizationcited by 51
  14. 2023A Study of Bayesian Neural Network Surrogates for Bayesian Optimizationcited by 50
  15. 2023AutoPEFT: Automatic Configuration Search for Parameter-Efficient Fine-Tuningcited by 49
  16. 2021Benchmarking the Performance of Bayesian Optimization across Multiple Experimental Materials Science Domainscited by 46
  17. 2021Combining Latent Space and Structured Kernels for Bayesian Optimization over Combinatorial Spacescited by 45
  18. 2022Joint Entropy Search for Multi-objective Bayesian Optimizationcited by 45
  19. 2021LassoBench: A High-Dimensional Hyperparameter Optimization Benchmark Suite for Lassocited by 41
  20. 2022Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomescited by 41
  21. 2022GAUCHE: A Library for Gaussian Processes in Chemistrycited by 40
  22. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  23. 2023Parameter-Efficient Fine-Tuning of LLaMA for the Clinical Domaincited by 38
  24. 2022Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimizationcited by 37
  25. 2022NAS-Bench-Suite: NAS Evaluation is (Now) Surprisingly Easycited by 36
  26. 2022Robust Multi-Objective Bayesian Optimization Under Input Noisecited by 36
  27. 2022Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterizationcited by 35
  28. 2021PointBA: Towards Backdoor Attacks in 3D Point Cloudcited by 34
  29. 2023Zeroth-Order Optimization Meets Human Feedback: Provable Learning via Ranking Oraclescited by 34
  30. 2021Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Informationcited by 33
  31. 2021Bayesian Optimization of Function Networkscited by 33
  32. 2024Standard Gaussian Process is All You Need for High-Dimensional Bayesian Optimizationcited by 33
  33. 2023Query-Efficient Black-Box Red Teaming via Bayesian Optimizationcited by 31
  34. 2024Quantum Architecture Search: A Surveycited by 31
  35. 2022Active Learning for Optimal Intervention Design in Causal Modelscited by 30
  36. 2024Model-Based Diffusion for Trajectory Optimizationcited by 30
  37. 2022A Survey of Methods for Automated Algorithm Configurationcited by 29
  38. 2022Discovering Many Diverse Solutions with Bayesian Optimizationcited by 29

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