# Expected Coordinate Improvement for High-Dimensional Bayesian Optimization

arXiv: https://arxiv.org/abs/2404.11917 · HTML: https://mlsanity.com/paper/2404.11917/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 68 references that are in the map.
- First posted on arXiv 18 Apr 2024.

## Builds on (most cited first, 22 of 22)

- [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)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2001.11659/) (2020)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [Batched High-dimensional Bayesian Optimization via Structural Kernel Learning](https://mlsanity.com/paper/1703.01973/) (2017)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)
- [High Dimensional Bayesian Optimization Using Dropout](https://mlsanity.com/paper/1802.05400/) (2018)
- [Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization](https://mlsanity.com/paper/2210.01628/) (2022)
- [On the choice of the low-dimensional domain for global optimization via random embeddings](https://mlsanity.com/paper/1704.05318/) (2017)
- [Good practices for Bayesian Optimization of high dimensional structured spaces](https://mlsanity.com/paper/2012.15471/) (2020)
- [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)
- [Bayesian Optimization with Dimension Scheduling: Application to Biological Systems](https://mlsanity.com/paper/1511.05385/) (2015)

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

- [A survey and benchmark of high-dimensional Bayesian optimization of discrete sequences](https://mlsanity.com/paper/2406.04739/) (2024)
- [Scalable Batch Bayesian Optimization Via Subspace Acquisition Functions](https://mlsanity.com/paper/2411.16206/) (2024)

## Abstract (arXiv)

Bayesian optimization (BO) algorithm is very popular for solving low-dimensional expensive optimization problems. Extending Bayesian optimization to high dimension is a meaningful but challenging task. One of the major challenges is that it is difficult to find good infill solutions as the acquisition functions are also high-dimensional. In this work, we propose the expected coordinate improvement (ECI) criterion for high-dimensional Bayesian optimization. The proposed ECI criterion measures the potential improvement we can get by moving the current best solution along one coordinate. The proposed approach selects the coordinate with the highest ECI value to refine in each iteration and covers all the coordinates gradually by iterating over the coordinates. The greatest advantage of the proposed ECI-BO (expected coordinate improvement based Bayesian optimization) algorithm over the standard BO algorithm is that the infill selection problem of the proposed algorithm is always a one-dimensional problem thus can be easily solved. Numerical experiments show that the proposed algorithm can achieve significantly better results than the standard BO algorithm and competitive results when compared with five state-of-the-art high-dimensional BOs. This work provides a simple but efficient approach for high-dimensional Bayesian optimization.