# Linear Embedding-based High-dimensional Batch Bayesian Optimization without Reconstruction Mappings

arXiv: https://arxiv.org/abs/2211.00947 · HTML: https://mlsanity.com/paper/2211.00947/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (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)
- [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)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration](https://mlsanity.com/paper/1304.5350/) (2013)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Batched Gaussian Process Bandit Optimization via Determinantal Point Processes](https://mlsanity.com/paper/1611.04088/) (2016)
- [On the choice of the low-dimensional domain for global optimization via random embeddings](https://mlsanity.com/paper/1704.05318/) (2017)
- [High Dimensional Bayesian Optimization via Supervised Dimension Reduction](https://mlsanity.com/paper/1907.08953/) (2019)
- [A warped kernel improving robustness in Bayesian optimization via random embeddings](https://mlsanity.com/paper/1411.3685/) (2014)
- [Optimization as Estimation with Gaussian Processes in Bandit Settings](https://mlsanity.com/paper/1510.06423/) (2015)
- [Semi-supervised Embedding Learning for High-dimensional Bayesian Optimization](https://mlsanity.com/paper/2005.14601/) (2020)
- [On Local Optimizers of Acquisition Functions in Bayesian Optimization](https://mlsanity.com/paper/1901.08350/) (2019)

## Built on by (most cited first, 1 of 1)

- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)

## Abstract (arXiv)

The optimization of high-dimensional black-box functions is a challenging problem. When a low-dimensional linear embedding structure can be assumed, existing Bayesian optimization (BO) methods often transform the original problem into optimization in a low-dimensional space. They exploit the low-dimensional structure and reduce the computational burden. However, we reveal that this approach could be limited or inefficient in exploring the high-dimensional space mainly due to the biased reconstruction of the high-dimensional queries from the low-dimensional queries. In this paper, we investigate a simple alternative approach: tackling the problem in the original high-dimensional space using the information from the learned low-dimensional structure. We provide a theoretical analysis of the exploration ability. Furthermore, we show that our method is applicable to batch optimization problems with thousands of dimensions without any computational difficulty. We demonstrate the effectiveness of our method on high-dimensional benchmarks and a real-world function.