  The cross-entropy (CE) method is a popular stochastic method for optimization
due to its simplicity and effectiveness. Designed for rare-event simulations
where the probability of a target event occurring is relatively small, the
CE-method relies on enough objective function calls to accurately estimate the
optimal parameters of the underlying distribution. Certain objective functions
may be computationally expensive to evaluate, and the CE-method could
potentially get stuck in local minima. This is compounded with the need to have
an initial covariance wide enough to cover the design space of interest. We
introduce novel variants of the CE-method to address these concerns. To
mitigate expensive function calls, during optimization we use every sample to
build a surrogate model to approximate the objective function. The surrogate
model augments the belief of the objective function with less expensive
evaluations. We use a Gaussian process for our surrogate model to incorporate
uncertainty in the predictions which is especially helpful when dealing with
sparse data. To address local minima convergence, we use Gaussian mixture
models to encourage exploration of the design space. We experiment with
evaluation scheduling techniques to reallocate true objective function calls
earlier in the optimization when the covariance is the largest. To test our
approach, we created a parameterized test objective function with many local
minima and a single global minimum. Our test function can be adjusted to
control the spread and distinction of the minima. Experiments were run to
stress the cross-entropy method variants and results indicate that the
surrogate model-based approach reduces local minima convergence using the same
number of function evaluations.

Machine Learning;Optimization and Control;Machine Learning