Sequential model-based optimization (SMBO) approaches are algorithms for solving problems that require computationally or otherwise expensive function evaluations. The key design principle of SMBO is a substitution of the true objective function by a surrogate, which is used to propose the point(s) to be evaluated next. SMBO algorithms are intrinsically modular, leaving the user with many important design choices. Significant research efforts go into understanding which settings perform best for which type of problems. Most works, however, focus on the choice of the model, the acquisition function, and the strategy used to optimize the latter. The choice of the initial sampling strategy, however, receives much less attention. Not surprisingly, quite diverging recommendations can be found in the literature. We analyze in this work how the size and the distribution of the initial sample influences the overall quality of the efficient global optimization~(EGO) algorithm, a well-known SMBO approach. While, overall, small initial budgets using Halton sampling seem preferable, we also observe that the performance landscape is rather unstructured. We furthermore identify several situations in which EGO performs unfavorably against random sampling. Both observations indicate that an adaptive SMBO design could be beneficial, making SMBO an interesting test-bed for automated algorithm design.

中文翻译：

---

初始设计策略及其对基于模型的序列优化的影响

基于序列模型的优化 (SMBO) 方法是用于解决需要计算或以其他方式进行昂贵的函数评估的问题的算法。SMBO 的关键设计原则是用代理替代真实目标函数，用于提出下一个要评估的点。SMBO 算法本质上是模块化的，为用户提供了许多重要的设计选择。重要的研究工作是了解哪种设置最适合哪种类型的问题。然而，大多数工作都集中在模型的选择、获取函数以及用于优化后者的策略上。然而，初始采样策略的选择受到的关注要少得多。毫不奇怪，在文献中可以找到非常不同的建议。我们在这项工作中分析了初始样本的大小和分布如何影响高效全局优化（EGO）算法的整体质量，这是一种众所周知的 SMBO 方法。虽然总体而言，使用 Halton 抽样的小初始预算似乎更可取，但我们也观察到性能前景相当非结构化。我们还确定了 EGO 对随机抽样不利的几种情况。两个观察结果都表明自适应 SMBO 设计可能是有益的，使 SMBO 成为自动化算法设计的一个有趣的测试平台。我们还观察到，性能环境相当非结构化。我们还确定了 EGO 对随机抽样不利的几种情况。两个观察结果都表明自适应 SMBO 设计可能是有益的，使 SMBO 成为自动化算法设计的一个有趣的测试平台。我们还观察到，性能环境相当非结构化。我们还确定了 EGO 对随机抽样不利的几种情况。两个观察结果都表明自适应 SMBO 设计可能是有益的，使 SMBO 成为自动化算法设计的一个有趣的测试平台。