  In many high-throughput experimental design settings, such as those common in
biochemical engineering, batched queries are more cost effective than
one-by-one sequential queries. Furthermore, it is often not possible to
directly choose items to query. Instead, the experimenter specifies a set of
constraints that generates a library of possible items, which are then selected
stochastically. Motivated by these considerations, we investigate \emph{Batched
Stochastic Bayesian Optimization} (BSBO), a novel Bayesian optimization scheme
for choosing the constraints in order to guide exploration towards items with
greater utility. We focus on \emph{site-saturation mutagenesis}, a prototypical
setting of BSBO in biochemical engineering, and propose a natural objective
function for this problem. Importantly, we show that our objective function can
be efficiently decomposed as a difference of submodular functions (DS), which
allows us to employ DS optimization tools to greedily identify sets of
constraints that increase the likelihood of finding items with high utility.
Our experimental results show that our algorithm outperforms common heuristics
on both synthetic and two real protein datasets.
