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A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization

Cheng, Nuojin ; Papenmeier, Leonard LU orcid ; Becker, Stephen and Nardi, Luigi LU (2025) 42nd International Conference on Machine Learning, ICML 2025 267. p.10106-10120
Abstract

Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function’s optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function,... (More)

Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function’s optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function, named Max-value Entropy Search. Building on this insight, we propose VES-Gamma, a novel acquisition function that balances the strengths of EI and MES. Extensive empirical evaluations across both low-and high-dimensional synthetic and real-world benchmarks demonstrate that VES-Gamma is competitive with state-of-the-art acquisition functions and in many cases outperforms EI and MES.

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author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings of Machine Learning Research
volume
267
pages
15 pages
publisher
ML Research Press
conference name
42nd International Conference on Machine Learning, ICML 2025
conference location
Vancouver, Canada
conference dates
2025-07-13 - 2025-07-19
external identifiers
  • scopus:105023640933
language
English
LU publication?
yes
id
a2d2c02f-889c-4a7b-8d8c-611f9d2a9b51
date added to LUP
2026-02-03 15:52:30
date last changed
2026-08-20 17:16:42
@inproceedings{a2d2c02f-889c-4a7b-8d8c-611f9d2a9b51,
  abstract     = {{<p>Bayesian optimization is a widely used method for optimizing expensive black-box functions, with Expected Improvement being one of the most commonly used acquisition functions. In contrast, information-theoretic acquisition functions aim to reduce uncertainty about the function’s optimum and are often considered fundamentally distinct from EI. In this work, we challenge this prevailing perspective by introducing a unified theoretical framework, Variational Entropy Search, which reveals that EI and information-theoretic acquisition functions are more closely related than previously recognized. We demonstrate that EI can be interpreted as a variational inference approximation of the popular information-theoretic acquisition function, named Max-value Entropy Search. Building on this insight, we propose VES-Gamma, a novel acquisition function that balances the strengths of EI and MES. Extensive empirical evaluations across both low-and high-dimensional synthetic and real-world benchmarks demonstrate that VES-Gamma is competitive with state-of-the-art acquisition functions and in many cases outperforms EI and MES.</p>}},
  author       = {{Cheng, Nuojin and Papenmeier, Leonard and Becker, Stephen and Nardi, Luigi}},
  booktitle    = {{Proceedings of Machine Learning Research}},
  language     = {{eng}},
  pages        = {{10106--10120}},
  publisher    = {{ML Research Press}},
  title        = {{A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization}},
  volume       = {{267}},
  year         = {{2025}},
}