Online Supplement to “The Knowledge-Gradient Policy for Correlated Normal Beliefs”

As discussed in Section 3 of the main paper, the KG policy posseses several optimality and convergence properties. First, it is optimal by construction when N = 1 (Remark 1). Second, the suboptimality gap between the values of the KG and the optimal policies narrows to 0 as N →∞ (Theorem 4). This is a convergence result, since it shows that when sampling under the KG policy we are guaranteed to eventually discover the alternative that is truly best. Third, the suboptimality gap is bounded for N between these two extremes (Theorem 5). Here, we discuss and prove these latter two results, discussing the convergence result in Section A.2, and the general bound on suboptimality in Section A.3. These results extend those proved in Frazier et al. (2008) for independent normal priors.