# Bayesian Optimization that Limits Search Region to Lower Dimensions Utilizing Local GPR

arXiv: https://arxiv.org/abs/2403.08331 · HTML: https://mlsanity.com/paper/2403.08331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 13 Mar 2024.

## Builds on (most cited first, 11 of 11)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [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)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Local Gaussian process approximation for large computer experiments](https://mlsanity.com/paper/1303.0383/) (2013)
- [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)
- [High Dimensional Bayesian Optimization Using Dropout](https://mlsanity.com/paper/1802.05400/) (2018)
- [Bayesian Optimization with Adaptive Kernels for Robot Control](https://mlsanity.com/paper/2402.07021/) (2024)

## Abstract (arXiv)

Optimization of product and system characteristics is required in many fields, including design and control. Bayesian optimization (BO) is often used when there are high observing costs, because BO theoretically guarantees an upper bound on regret. However, computational costs increase exponentially with the number of parameters to be optimized, decreasing search efficiency. We propose a BO that limits the search region to lower dimensions and utilizes local Gaussian process regression (LGPR) to scale the BO to higher dimensions. LGPR treats the low-dimensional search region as "local," improving prediction accuracies there. The LGPR model is trained on a local subset of data specific to that region. This improves prediction accuracy and search efficiency and reduces the time complexity of matrix inversion in the Gaussian process regression. In evaluations with 20D Ackley and Rosenbrock functions, search efficiencies are equal to or higher than those of the compared methods, improved by about 69% and 40% from the case without LGPR. We apply our method to an automatic design task for a power semiconductor device. We successfully reduce the specific on-resistance to 25% better than a conventional method and 3.4% better than without LGPR.