  We consider derivative-free black-box global optimization of expensive noisy
functions, when most of the randomness in the objective is produced by a few
influential scalar random inputs. We present a new Bayesian global optimization
algorithm, called Stratified Bayesian Optimization (SBO), which uses this
strong dependence to improve performance. Our algorithm is similar in spirit to
stratification, a technique from simulation, which uses strong dependence on a
categorical representation of the random input to reduce variance. We
demonstrate in numerical experiments that SBO outperforms state-of-the-art
Bayesian optimization benchmarks that do not leverage this dependence.
