Optimal learning with a local parametric belief model (Q746825)

The authors are interested in maximizing an unknown function where observations are noisy and expensive to compute. They derive a knowledge-gradient policy for correlated alternatives. Instead of a known covariance matrix they use a statistical method (called Dirichlet cloud radial basis function; DC-RBF) to define local regions and approximate the local covariance structures. The method then uses a weighted sum of the local models to estimate the global function. In addition, they propose a hierarchical approach that combines multiple levels of DC-RBF with different threshold distances. Experimental work suggests that the method adapts to a range of arbitrary, continuous functions, and appears to reliably find the optimal solution. Moreover, the policy is shown to be asymptotically optimal.