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Abstract:
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Optimizing a black-box function is challenging when the function is non-linear and dependent on a large number of input variables. Expected improvement (EI) algorithms balance exploration of the design space and identification of a global maximizer, but struggle in high dimensions. Based on response surface methodology, reducing the dimension of the design space to include only the most important variables improves estimation and leads to quicker identification of the global maximizer. Current variable selection techniques are global; a variable is either in or out of the design matrix. It is likely, however, that in local neighborhoods around the global maximizer, only a few variables are important. In this paper, we define a measure of local importance to identify which variables are locally active and use this measure to efficiently search the design space to estimate the global maximizer. We develop SOLID, Sequential Optimization of Locally Important Dimensions, which does global variable selection, fixes the values of the locally inactive variables, hones in on a smaller subset of the design space, and optimizes over the locally active variables to identify the global maxim
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