# Exploring Exploration in Bayesian Optimization

arXiv: https://arxiv.org/abs/2502.08208 · HTML: https://mlsanity.com/paper/2502.08208/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 74 references that are in the map.
- First posted on arXiv 12 Feb 2025.

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

- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Algorithms for multi-armed bandit problems](https://mlsanity.com/paper/1402.6028/) (2014)
- [Pathwise Conditioning of Gaussian Processes](https://mlsanity.com/paper/2011.04026/) (2020)
- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Greed is Good: Exploration and Exploitation Trade-offs in Bayesian Optimisation](https://mlsanity.com/paper/1911.12809/) (2019)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Parallel Bayesian Global Optimization of Expensive Functions](https://mlsanity.com/paper/1602.05149/) (2016)
- [Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees](https://mlsanity.com/paper/2006.15779/) (2020)
- [LassoBench: A High-Dimensional Hyperparameter Optimization Benchmark Suite for Lasso](https://mlsanity.com/paper/2111.02790/) (2021)
- [Efficient multivariate entropy estimation via k-nearest neighbour distances](https://mlsanity.com/paper/1606.00304/) (2016)
- [Epsilon-Greedy Thompson Sampling to Bayesian Optimization](https://mlsanity.com/paper/2403.00540/) (2024)
- [A sequential Monte Carlo approach to Thompson sampling for Bayesian optimization](https://mlsanity.com/paper/1604.00169/) (2016)
- [PI is back! Switching Acquisition Functions in Bayesian Optimization](https://mlsanity.com/paper/2211.01455/) (2022)
- [Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms](https://mlsanity.com/paper/2306.16998/) (2023)
- [A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization](https://mlsanity.com/paper/2501.18756/) (2025)
- [On a Traveling Salesman Problem for Points in the Unit Cube](https://mlsanity.com/paper/2310.02839/) (2023)

## Built on by (most cited first, 9 of 9)

- [Understanding High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2502.09198/) (2025)
- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [Dynamic Priors in Bayesian Optimization for Hyperparameter Optimization](https://mlsanity.com/paper/2511.02570/) (2025)
- [Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2604.08891/) (2026)
- [BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization](https://mlsanity.com/paper/2508.02332/) (2025)
- [Maximizing Reliability with Bayesian Optimization](https://mlsanity.com/paper/2602.02432/) (2026)
- [Optimization of time-consuming experimental conditions using pseudo-experimental data guided by adaptive polynomial regression](https://mlsanity.com/paper/2607.22238/) (2026)
- [Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search](https://mlsanity.com/paper/2609.34281/) (2026)
- [Isotropic Gaussian Processes Improve Vanilla Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2610.05780/) (2026)

## Abstract (arXiv)

A well-balanced exploration-exploitation trade-off is crucial for successful acquisition functions in Bayesian optimization. However, there is a lack of quantitative measures for exploration, making it difficult to analyze and compare different acquisition functions. This work introduces two novel approaches - observation traveling salesman distance and observation entropy - to quantify the exploration characteristics of acquisition functions based on their selected observations. Using these measures, we examine the explorative nature of several well-known acquisition functions across a diverse set of black-box problems, uncover links between exploration and empirical performance, and reveal new relationships among existing acquisition functions. Beyond enabling a deeper understanding of acquisition functions, these measures also provide a foundation for guiding their design in a more principled and systematic manner.