# Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOB

arXiv: https://arxiv.org/abs/2303.00890 · HTML: https://mlsanity.com/paper/2303.00890/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 72 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 24 of 24)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Auto-Keras: An Efficient Neural Architecture Search System](https://mlsanity.com/paper/1806.10282/) (2018)
- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets](https://mlsanity.com/paper/1605.07079/) (2016)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)
- [TREGO: a Trust-Region Framework for Efficient Global Optimization](https://mlsanity.com/paper/2101.06808/) (2021)
- [IOHprofiler: A Benchmarking and Profiling Tool for Iterative Optimization Heuristics](https://mlsanity.com/paper/1810.05281/) (2018)
- [IOHanalyzer: Detailed Performance Analyses for Iterative Optimization Heuristics](https://mlsanity.com/paper/2007.03953/) (2020)
- [Randomly Projected Additive Gaussian Processes for Regression](https://mlsanity.com/paper/1912.12834/) (2019)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [High Dimensional Bayesian Optimization Assisted by Principal Component Analysis](https://mlsanity.com/paper/2007.00925/) (2020)
- [Semi-supervised Embedding Learning for High-dimensional Bayesian Optimization](https://mlsanity.com/paper/2005.14601/) (2020)
- [Bayesian Optimization in Materials Science: A Survey](https://mlsanity.com/paper/2108.00002/) (2021)
- [Modeling and Optimization with Gaussian Processes in Reduced Eigenbases -- Extended Version](https://mlsanity.com/paper/1908.11272/) (2019)
- [High Dimensional Bayesian Optimization with Kernel Principal Component Analysis](https://mlsanity.com/paper/2204.13753/) (2022)

## Built on by (most cited first, 19 of 19)

- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Pretrained Optimization Model for Zero-Shot Black Box Optimization](https://mlsanity.com/paper/2405.03728/) (2024)
- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [LLaMEA-BO: A Large Language Model Evolutionary Algorithm for Automatically Generating Bayesian Optimization Algorithms](https://mlsanity.com/paper/2505.21034/) (2025)
- [High Dimensional Bayesian Optimization using Lasso Variable Selection](https://mlsanity.com/paper/2504.01743/) (2025)
- [LABCAT: Locally adaptive Bayesian optimization using principal-component-aligned trust regions](https://mlsanity.com/paper/2311.11328/) (2023)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [High-Dimensional Bayesian Optimisation with Large-Scale Constraints -- An Application to Aeroelastic Tailoring](https://mlsanity.com/paper/2312.08891/) (2023)
- [SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations](https://mlsanity.com/paper/2511.00685/) (2025)
- [Automated Discovery of Laser Dicing Processes with Bayesian Optimization for Semiconductor Manufacturing](https://mlsanity.com/paper/2511.23141/) (2025)
- [Frugal Bayesian Optimization: Scalable Surrogates for Data- and Resource-Limited Discovery](https://mlsanity.com/paper/2607.29225/) (2026)
- [Adaptive Replication Strategies in Trust-Region-Based Bayesian Optimization of Stochastic Functions](https://mlsanity.com/paper/2504.20527/) (2025)
- [Methods for Multi-objective Optimization PID Controller for quadrotor UAVs](https://mlsanity.com/paper/2509.17423/) (2025)
- [Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems](https://mlsanity.com/paper/2509.21725/) (2025)
- [Trust Region-Based Bayesian Optimisation to Discover Diverse Solutions](https://mlsanity.com/paper/2511.00750/) (2025)
- [Improving through Interaction: Searching Behavioral Representation Spaces with CMA-ES-IG](https://mlsanity.com/paper/2603.09011/) (2026)
- [Automated Random Embedding for Practical Bayesian Optimization with Unknown Effective Dimension](https://mlsanity.com/paper/2605.23473/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)
- [MF-SCBO : Multi-fidelity Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2609.29941/) (2026)

## Abstract (arXiv)

Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate, and hence admit only small evaluation budgets. BO is particularly popular for solving numerical optimization problems in industry, where the evaluation of objective functions often relies on time-consuming simulations or physical experiments. However, many industrial problems depend on a large number of parameters. This poses a challenge for BO algorithms, whose performance is often reported to suffer when the dimension grows beyond 15 variables. Although many new algorithms have been proposed to address this problem, it is not well understood which one is the best for which optimization scenario. In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at increasing dimensionality, ranging from 10 to 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.