  Stochastic computer simulations enable users to gain new insights into
complex physical systems. Optimization is a common problem in this context:
users seek to find model inputs that maximize the expected value of an
objective function. The objective function, however, is time-intensive to
evaluate, and cannot be directly measured. Instead, the stochastic nature of
the model means that individual realizations are corrupted by noise. More
formally, we consider the problem of optimizing the expected value of an
expensive black-box function with continuously-differentiable mean, from which
observations are corrupted by Gaussian noise. We present Parallel Simultaneous
Perturbation Optimization (PSPO), which extends a well-known stochastic
optimization algorithm, simultaneous perturbation stochastic approximation, in
several important ways. Our modifications allow the algorithm to fully take
advantage of parallel computing resources, like high-performance cloud
computing. The resulting PSPO algorithm takes fewer time-consuming iterations
to converge, automatically chooses the step size, and can vary the error
tolerance by step. Theoretical results are supported by a numerical example. To
demonstrate the performance of the algorithm, we implemented the algorithm to
maximize the pseudo-likelihood of a stochastic epidemiological model to data of
a measles outbreak.
