  One-shot decision making is required in situations in which we can evaluate a
fixed number of solution candidates but do not have any possibility for
further, adaptive sampling. Such settings are frequently encountered in neural
network design, hyper-parameter optimization, and many simulation-based
real-world optimization tasks, in which evaluations are costly and time sparse.
It seems intuitive that well-distributed samples should be more meaningful in
one-shot decision making settings than uniform or grid-based samples, since
they show a better coverage of the decision space. In practice, quasi-random
designs such as Latin Hypercube Samples and low-discrepancy point sets form
indeed the state of the art, as confirmed by a number of recent studies and
competitions. In this work we take a closer look into the correlation between
the distribution of the quasi-random designs and their performance in one-shot
decision making tasks, with the goal to investigate whether the assumed
correlation between uniform distribution and performance can be confirmed. We
study three different decision tasks: classic one-shot optimization (only the
best sample matters), one-shot optimization with surrogates (allowing to use
surrogate models for selecting a design that need not necessarily be one of the
evaluated samples), and one-shot regression (i.e., function approximation, with
minimization of mean squared error as objective). Our results confirm an
advantage of low-discrepancy designs for all three settings. The overall
correlation, however, is rather weak. We complement our study by evolving
problem-specific samples that show significantly better performance for the
regression task than the standard approaches based on low-discrepancy
sequences, giving strong indication that significant performance gains over
state-of-the-art one-shot sampling techniques are possible.
