A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimization
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 func- tions aim to reduce uncertainty about the func- tion’s optimum and are often considered fun- damentally distinct from EI. In this work, we challenge this prevailing perspective by intro- ducing a unified theoretical framework, Varia- tional 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 pop- ular 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 evalua- tions across both low- and high-dimensional syn- thetic 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.
Keywords
Bayesian Optimization