# Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testing

arXiv: https://arxiv.org/abs/2504.06111 · HTML: https://mlsanity.com/paper/2504.06111/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 54 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 27 of 27)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Neural Architecture Search with Bayesian Optimisation and Optimal Transport](https://mlsanity.com/paper/1802.07191/) (2018)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [Bayesian Optimization in AlphaGo](https://mlsanity.com/paper/1812.06855/) (2018)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [LassoBench: A High-Dimensional Hyperparameter Optimization Benchmark Suite for Lasso](https://mlsanity.com/paper/2111.02790/) (2021)
- [Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization](https://mlsanity.com/paper/2210.01628/) (2022)
- [Practical Design Space Exploration](https://mlsanity.com/paper/1810.05236/) (2018)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Bounce: Reliable High-Dimensional Bayesian Optimization for Combinatorial and Mixed Spaces](https://mlsanity.com/paper/2307.00618/) (2023)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [Sequential Learning of Active Subspaces](https://mlsanity.com/paper/1907.11572/) (2019)
- [Unbounded Bayesian Optimization via Regularization](https://mlsanity.com/paper/1508.03666/) (2015)
- [Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection](https://mlsanity.com/paper/2109.09264/) (2021)
- [Bayesian Optimization with Dimension Scheduling: Application to Biological Systems](https://mlsanity.com/paper/1511.05385/) (2015)
- [Learning Skill-based Industrial Robot Tasks with User Priors](https://mlsanity.com/paper/2208.01605/) (2022)
- [Noisy Adaptive Group Testing using Bayesian Sequential Experimental Design](https://mlsanity.com/paper/2004.12508/) (2020)

## Built on by (most cited first, 2 of 2)

- [We Still Don't Understand High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2512.00170/) (2025)
- [Isotropic Gaussian Processes Improve Vanilla Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2610.05780/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO ) is an effective method for optimizing expensive-to-evaluate black-box functions. While high-dimensional problems can be particularly challenging, due to the multitude of parameter choices and the potentially high number of data points required to fit the model, this limitation can be addressed if the problem satisfies simplifying assumptions. Axis-aligned subspace approaches, where few dimensions have a significant impact on the objective, motivated several algorithms for high-dimensional BO . However, the validity of this assumption is rarely verified, and the assumption is rarely exploited to its full extent. We propose a group testing ( GT) approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective, then terminates once active dimensions are identified. To that end, we extend the well-established GT theory to functions over continuous domains. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By leveraging the axis-aligned subspace assumption, GTBO outperforms state-of-the-art methods on benchmarks satisfying the assumption of axis-aligned subspaces, while offering improved interpretability.