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Unified framework for entropy search and expected improvement in Bayesian optimization

Cheng, Nuojin ; Papenmeier, Leonard LU orcid ; Becker, Stephen and Nardi, Luigi LU (2025)
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, named... (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. (Less)
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author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
in press
subject
host publication
Forty-Second International Conference on Machine Learning
pages
13 pages
language
English
LU publication?
yes
id
4e1e1448-f73d-44cc-a995-027c7bbe4a38
alternative location
https://arxiv.org/abs/2501.18756
date added to LUP
2025-05-07 15:08:36
date last changed
2025-05-15 11:05:12
@inproceedings{4e1e1448-f73d-44cc-a995-027c7bbe4a38,
  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, 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.}},
  author       = {{Cheng, Nuojin and Papenmeier, Leonard and Becker, Stephen and Nardi, Luigi}},
  booktitle    = {{Forty-Second International Conference on Machine Learning}},
  language     = {{eng}},
  title        = {{Unified framework for entropy search and expected improvement in Bayesian optimization}},
  url          = {{https://arxiv.org/abs/2501.18756}},
  year         = {{2025}},
}