# High-Dimensional Bayesian Optimization Using Both Random and Supervised Embeddings

arXiv: https://arxiv.org/abs/2502.00854 · HTML: https://mlsanity.com/paper/2502.00854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 2 Feb 2025.

## Builds on (most cited first, 5 of 5)

- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [TREGO: a Trust-Region Framework for Efficient Global Optimization](https://mlsanity.com/paper/2101.06808/) (2021)
- [On the choice of the low-dimensional domain for global optimization via random embeddings](https://mlsanity.com/paper/1704.05318/) (2017)
- [An efficient application of Bayesian optimization to an industrial MDO framework for aircraft design](https://mlsanity.com/paper/2006.08434/) (2020)
- [High-dimensional mixed-categorical Gaussian processes with application to multidisciplinary design optimization for a green aircraft](https://mlsanity.com/paper/2311.06130/) (2023)

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

- [Frequency-aware Surrogate Modeling With SMT Kernels For Advanced Data Forecasting](https://mlsanity.com/paper/2507.09694/) (2025)
- [Efficient multidisciplinary design via Bayesian optimization](https://mlsanity.com/paper/2607.22560/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is one of the most powerful strategies to solve computationally expensive-to-evaluate blackbox optimization problems. However, BO methods are conventionally used for optimization problems of small dimension because of the curse of dimensionality. In this paper, a high-dimensionnal optimization method incorporating linear embedding subspaces of small dimension is proposed to efficiently perform the optimization. An adaptive learning strategy for these linear embeddings is carried out in conjunction with the optimization. The resulting BO method, named efficient global optimization coupled with random and supervised embedding (EGORSE), combines in an adaptive way both random and supervised linear embeddings. EGORSE has been compared to state-of-the-art algorithms and tested on academic examples with a number of design variables ranging from 10 to 600. The obtained results show the high potential of EGORSE to solve high-dimensional blackbox optimization problems, in terms of both CPU time and the limited number of calls to the expensive blackbox simulation.