  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.
