{
  "id": "2501.18756",
  "version": "v1",
  "published": "2025-01-30T21:15:00.000Z",
  "updated": "2025-01-30T21:15:00.000Z",
  "title": "A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization",
  "authors": [
    "Nuojin Cheng",
    "Leonard Papenmeier",
    "Stephen Becker",
    "Luigi Nardi"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.OC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-30T21:15:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bayesian optimization",
      "expected improvement",
      "unified framework",
      "information-theoretic acquisition functions aim",
      "popular information-theoretic acquisition function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}