  Bayesian optimization is a widely used technique for optimizing black-box
functions, with Expected Improvement (EI) being the most commonly utilized
acquisition function in this domain. While EI is often viewed as distinct from
other information-theoretic acquisition functions, such as entropy search (ES)
and max-value entropy search (MES), our work reveals that EI can be considered
a special case of MES when approached through variational inference (VI). In
this context, we have developed the Variational Entropy Search (VES)
methodology and the VES-Gamma algorithm, which adapts EI by incorporating
principles from information-theoretic concepts. The efficacy of VES-Gamma is
demonstrated across a variety of test functions and read datasets, highlighting
its theoretical and practical utilities in Bayesian optimization scenarios.
