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We propose a sequential learning policy for noisy discrete globaloptimization and ranking and selection (R\&S) problems with high dimensionalsparse belief functions, where there are hundreds or even thousands offeatures, but only a small portion of these features contain explanatory power.We aim to identify the sparsity pattern and select the best alternative beforethe finite budget is exhausted. We derive a knowledge gradient policy forsparse linear models (KGSpLin) with group Lasso penalty. This policy is aunique and novel hybrid of Bayesian R\&S with frequentist learning.Particularly, our method naturally combines B-spline basis expansion andgeneralizes to the nonparametric additive model (KGSpAM) and functional ANOVAmodel. Theoretically, we provide the estimation error bounds of the posteriormean estimate and the functional estimate. Controlled experiments show that thealgorithm efficiently learns the correct set of nonzero parameters even whenthe model is imbedded with hundreds of dummy parameters. Also it outperformsthe knowledge gradient for a linear model.

The Knowledge Gradient Policy Using A Sparse Additive Belief Model