Expensive Black-Box Model Optimization Via a Gold Rush Policy

The optimization of black-box models is a challenging task owing to the lack of analytic gradient information and structural information about the underlying function, and also due often to significant run times. A common approach to tackling such problems is the implementation of Bayesian global optimization techniques. However, these techniques often rely on surrogate modeling strategies that endow the approximation of the underlying expensive function with nonexistent features. Further, these techniques tend to push new queries away from previously queried design points, making it difficult to locate an optimum point that rests near a previous model evaluation. To overcome these issues, we propose a gold rush (GR) policy that relies on purely local information to identify the next best design alternative to query. The method employs a surrogate constructed pointwise, that adds no additional features to the approximation. The result is a policy that performs well in comparison to state of the art Bayesian global optimization methods on several benchmark problems. The policy is also demonstrated on a constrained optimization problem using a penalty method.