  Driven by the need for parallelizable hyperparameter optimization methods,
this paper studies \emph{open loop} search methods: sequences that are
predetermined and can be generated before a single configuration is evaluated.
Examples include grid search, uniform random search, low discrepancy sequences,
and other sampling distributions. In particular, we propose the use of
$k$-determinantal point processes in hyperparameter optimization via random
search. Compared to conventional uniform random search where hyperparameter
settings are sampled independently, a $k$-DPP promotes diversity. We describe
an approach that transforms hyperparameter search spaces for efficient use with
a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm
which can sample from $k$-DPPs defined over any space from which uniform
samples can be drawn, including spaces with a mixture of discrete and
continuous dimensions or tree structure. Our experiments show significant
benefits in realistic scenarios with a limited budget for training supervised
learners, whether in serial or parallel.
