A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization
This work addresses a theoretical gap for researchers in Bayesian optimization, though it is incremental as it builds on existing methods.
The paper tackles the perceived distinction between Expected Improvement and information-theoretic acquisition functions in Bayesian optimization by introducing a unified framework, Variational Entropy Search, showing that EI approximates Max-value Entropy Search and proposing VES-Gamma, which outperforms EI and MES in many benchmarks.
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.