  Optimization is becoming increasingly common in scientific and engineering
domains. Oftentimes, these problems involve various levels of stochasticity or
uncertainty in generating proposed solutions. Therefore, optimization in these
scenarios must consider this stochasticity to properly guide the design of
future experiments. Here, we adapt Bayesian optimization to handle uncertain
outcomes, proposing a new framework called stochastic sampling Bayesian
optimization (SSBO). We show that the bounds on expected regret for an upper
confidence bound search in SSBO resemble those of earlier Bayesian optimization
approaches, with added penalties due to the stochastic generation of inputs.
Additionally, we adapt existing batch optimization techniques to properly limit
the myopic decision making that can arise when selecting multiple instances
before feedback. Finally, we show that SSBO techniques properly optimize a set
of standard optimization problems as well as an applied problem inspired by
bioengineering.
