Derivation of Closed Form of Expected Improvement for Gaussian Process Trained on Log-Transformed Objective

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1. Verfasser: Watanabe, Shuhei
Format: Preprint
Veröffentlicht: 2024
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author Watanabe, Shuhei
author_facet Watanabe, Shuhei
contents Expected Improvement (EI) is arguably the most widely used acquisition function in Bayesian optimization. However, it is often challenging to enhance the performance with EI due to its sensitivity to numerical precision. Previously, Hutter et al. (2009) tackled this problem by using Gaussian process trained on the log-transformed objective function and it was reported that this trick improves the predictive accuracy of GP, leading to substantially better performance. Although Hutter et al. (2009) offered the closed form of their EI, its intermediate derivation has not been provided so far. In this paper, we give a friendly derivation of their proposition.
format Preprint
id arxiv_https___arxiv_org_abs_2411_18095
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Derivation of Closed Form of Expected Improvement for Gaussian Process Trained on Log-Transformed Objective
Watanabe, Shuhei
Machine Learning
Artificial Intelligence
Expected Improvement (EI) is arguably the most widely used acquisition function in Bayesian optimization. However, it is often challenging to enhance the performance with EI due to its sensitivity to numerical precision. Previously, Hutter et al. (2009) tackled this problem by using Gaussian process trained on the log-transformed objective function and it was reported that this trick improves the predictive accuracy of GP, leading to substantially better performance. Although Hutter et al. (2009) offered the closed form of their EI, its intermediate derivation has not been provided so far. In this paper, we give a friendly derivation of their proposition.
title Derivation of Closed Form of Expected Improvement for Gaussian Process Trained on Log-Transformed Objective
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2411.18095