Not yet reviewed by Pith; the record is open.

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.