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.

翻译：贝叶斯优化是一种广泛用于优化黑盒函数的技术，其中期望改进(EI)是该领域最常用的采集函数。虽然EI通常被视为与熵搜索(ES)和最大值熵搜索(MES)等其他信息论采集函数不同，但我们的工作揭示，通过变分推理(VI)方法，EI可以被视为MES的一种特例。在此背景下，我们开发了变分熵搜索(VES)方法论和VES-Gamma算法，该算法通过融合信息论概念的原理对EI进行调整。VES-Gamma的有效性已在多种测试函数和真实数据集上得到验证，突显了其在贝叶斯优化场景中的理论和实践效用。