Surrogate-based optimization relies on so-called infill criteria (acquisition functions) to decide which point to evaluate next. When Kriging is used as the surrogate model of choice (also called Bayesian optimization), one of the most frequently chosen criteria is expected improvement. We argue that the popularity of expected improvement largely relies on its theoretical properties rather than empirically validated performance. Few results from the literature show evidence, that under certain conditions, expected improvement may perform worse than something as simple as the predicted value of the surrogate model. We benchmark both infill criteria in an extensive empirical study on the `BBOB' function set. This investigation includes a detailed study of the impact of problem dimensionality on algorithm performance. The results support the hypothesis that exploration loses importance with increasing problem dimensionality. A statistical analysis reveals that the purely exploitative search with the predicted value criterion performs better on most problems of five or higher dimensions. Possible reasons for these results are discussed. In addition, we give an in-depth guide for choosing the infill criteria based on prior knowledge about the problem at hand, its dimensionality, and the available budget.

中文翻译：

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基于代理的优化中的预期改进与预测值

基于代理的优化依赖于所谓的填充标准（获取函数）来决定接下来评估哪个点。当克里金法用作选择的替代模型（也称为贝叶斯优化）时，最常选择的标准之一是预期改进。我们认为预期改进的流行在很大程度上取决于其理论特性，而不是经验验证的性能。很少有文献结果表明证据表明，在某些条件下，预期改进的表现可能比代理模型的预测值这样简单。我们在对“BBOB”函数集的广泛实证研究中对这两个填充标准进行了基准测试。这项调查包括对问题维度对算法性能影响的详细研究。结果支持了探索随着问题维度的增加而失去重要性的假设。统计分析表明，使用预测值标准的纯粹开发性搜索在五个或更高维度的大多数问题上表现更好。讨论了这些结果的可能原因。此外，我们根据手头问题、其维度和可用预算的先验知识，为选择填充标准提供了深入的指导。