Ranking and Contextual Selection

This paper proposes a new ranking-and-selection procedure, called ranking and contextual selection, in which covariates provide context for data-driven decisions. Our procedure optimizes over a set of covariate design points off-line and then, given an actual observation of the covariate, makes an online decision based on classification—a distinctly new approach. We prove the existence of an experimental design that yields a pointwise probability of good selection guarantee and derive a postexperiment assessment of our procedure that provides an optimality gap upper bound with guaranteed coverage for decisions with respect to future covariates. We illustrate ranking and contextual selection with an application to assortment optimization using data available from Yahoo!.