TITLE:
Finding and Choosing among Multiple Optima
AUTHORS:
John Guenther, Herbert K. H. Lee, Genetha A. Gray
KEYWORDS:
Bayesian Statistics; Treed Gaussian Process; Emulator; Decision Theory; Optimization
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.2,
January
20,
2014
ABSTRACT: Black box functions, such
as computer experiments, often have multiple optima over the input space of the
objective function. While traditional optimization routines focus on finding a
single best optimum, we sometimes want to consider the relative merits of
multiple optima. First we need a search algorithm that can identify multiple local optima. Then we consider that
blindly choosing the global optimum may not always be best. In some cases, the
global optimum may not be robust to small deviations in the inputs, which could
lead to output values far from the optimum. In those cases, it would be better
to choose a slightly less extreme optimum that allows for input deviation with
small change in the output; such an optimum would be considered more robust. We
use a Bayesian decision theoretic approach to develop a utility function for
selecting among multiple optima.