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Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization

arXiv 2001.11659 ↗First posted 31 Jan 2020stat.ML cs.LGcited by 89

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Abstract (arXiv)

Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered in existing literature is to embed the high-dimensional space in a lower-dimensional manifold, often via a random linear embedding. In this paper, we identify several crucial issues and misconceptions about the use of linear embeddings for BO. We study the properties of linear embeddings from the literature and show that some of the design choices in current approaches adversely impact their performance. We show empirically that properly addressing these issues significantly improves the efficacy of linear embeddings for BO on a range of problems, including learning a gait policy for robot locomotion.

Key facts. Cited by 89 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Jan 2020.

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Citing papers per year: 2021: 11; 2022: 16; 2023: 18; 2024: 18; 2025: 18; 2026: 8.

89 papers.

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  1. 2022Black-Box Tuning for Language-Model-as-a-Servicecited by 254
  2. 2021High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspacescited by 139
  3. 2021Multi-Objective Bayesian Optimization over High-Dimensional Search Spacescited by 87
  4. 2024Vanilla Bayesian Optimization Performs Great in High Dimensionscited by 87
  5. 2022Recent Advances in Bayesian Optimizationcited by 74
  6. 2021High-Dimensional Bayesian Optimisation with Variational Autoencoders and Deep Metric Learningcited by 54
  7. 2021Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spacescited by 51
  8. 2023Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspacescited by 50
  9. 2021LassoBench: A High-Dimensional Hyperparameter Optimization Benchmark Suite for Lassocited by 41
  10. 2022Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimizationcited by 37
  11. 2023Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?cited by 35
  12. 2021Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Informationcited by 33
38 more
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  2. 2022Discovering Many Diverse Solutions with Bayesian Optimizationcited by 29
  3. 2023Gradient-Free Textual Inversioncited by 28
  4. 2023Bounce: Reliable High-Dimensional Bayesian Optimization for Combinatorial and Mixed Spacescited by 27
  5. 2022Thinking inside the box: A tutorial on grey-box Bayesian optimizationcited by 26
  6. 2023Bayesian Optimization over High-Dimensional Combinatorial Spaces via Dictionary-based Embeddingscited by 24
  7. 2024A survey and benchmark of high-dimensional Bayesian optimization of discrete sequencescited by 22
  8. 2025Understanding High-Dimensional Bayesian Optimizationcited by 19
  9. 2023Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOBcited by 18
  10. 2024Bayesian optimization as a flexible and efficient design framework for sustainable process systemscited by 15
  11. 2021Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selectioncited by 12
  12. 2025Posterior Inference with Diffusion Models for High-dimensional Black-box Optimizationcited by 12
  13. 2024Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimizationcited by 9
  14. 2025We Still Don't Understand High-Dimensional Bayesian Optimizationcited by 9
  15. 2023Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimizationcited by 8
  16. 2023Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimationcited by 8
  17. 2023Batch Bayesian Optimization for Replicable Experimental Designcited by 7
  18. 2023Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasmacited by 6
  19. 2025NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Informationcited by 6
  20. 2022MBORE: Multi-objective Bayesian Optimisation by Density-Ratio Estimationcited by 5
  21. 2022ODBO: Bayesian Optimization with Search Space Prescreening for Directed Protein Evolutioncited by 5
  22. 2022Investigating Bayesian optimization for expensive-to-evaluate black box functions: Application in fluid dynamicscited by 5
  23. 2023Unleashing the Potential of Acquisition Functions in High-Dimensional Bayesian Optimizationcited by 5
  24. 2023High-Dimensional Bayesian Optimization via Semi-Supervised Learning with Optimized Unlabeled Data Samplingcited by 5
  25. 2023High-dimensional Bayesian Optimization with Group Testingcited by 5
  26. 2023Joint Composite Latent Space Bayesian Optimizationcited by 5
  27. 2024High-dimensional Bayesian Optimization via Covariance Matrix Adaptation Strategycited by 5
  28. 2024Model Fusion through Bayesian Optimization in Language Model Fine-Tuningcited by 5
  29. 2023Quantum approximate optimization via learning-based adaptive optimizationcited by 4
  30. 2024Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systemscited by 4
  31. 2022B2EA: An Evolutionary Algorithm Assisted by Two Bayesian Optimization Modules for Neural Architecture Searchcited by 3
  32. 2022Learning Representation for Bayesian Optimization with Collision-free Regularizationcited by 3
  33. 2022Sample-Efficient Optimisation with Probabilistic Transformer Surrogatescited by 3
  34. 2024No-Regret Learning of Nash Equilibrium for Black-Box Games via Gaussian Processescited by 3
  35. 2025High Dimensional Bayesian Optimization using Lasso Variable Selectioncited by 3
  36. 2021Bayesian Optimization with Clustering and Rollback for CNN Auto Pruningcited by 2
  37. 2021Predicting the utility of search spaces for black-box optimization: a simple, budget-aware approachcited by 2
  38. 2022Bayesian Optimization with Informative Covariancecited by 2

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