Field experiments and computer simulations are effective but time-consuming methods of measuring the quality of engineered systems at different settings. To reduce the total time required, experimenters may employ Bayesian optimization, which is parsimonious with measurements, and take measurements of multiple settings simultaneously, in a batch. In practice, experimenters use very few batches, thus, it is imperative that each batch be as informative as possible. Typically, the initial batch in a Batch Bayesian Optimization (BBO) is constructed from a quasi-random sample of settings values. We propose a batch-design acquisition function, Minimal Terminal Variance (MTV), that designs a batch by optimization rather than random sampling. MTV adapts a design criterion function from Design of Experiments, called I-Optimality, which minimizes the variance of the post-evaluation estimates of quality, integrated over the entire space of settings. MTV weights the integral by the probability that a setting is optimal, making it able to design not only an initial batch but all subsequent batches, as well. Applicability to both initialization and subsequent batches is novel among acquisition functions. Numerical experiments on test functions and simulators show that MTV compares favorably to other BBO methods.

翻译：现场实验和计算机模拟是测量工程系统在不同设置下质量的有效但耗时的方法。为减少所需总时间，实验人员可采用对测量次数要求较为节俭的贝叶斯优化，并以批次方式同时测量多个设置。实践中，实验人员使用的批次非常少，因此每一批次必须尽可能提供更多信息。在批量贝叶斯优化(BBO)中，初始批次通常基于设置的准随机样本构建。我们提出一种批次设计采集函数——最小终末方差(MTV)，通过优化而非随机采样来设计批次。MTV借鉴了实验设计中的设计准则函数I-最优性，该函数最小化质量评估后的方差在全部设置空间上的积分。MTV以设置最优的概率对积分进行加权，使其不仅能设计初始批次，还能设计所有后续批次。这种对初始化和后续批次的普适适用性是采集函数领域的新颖特性。对测试函数和模拟器的数值实验表明，MTV相较于其他BBO方法具有更优表现。