1 research outputs found
Selection of the Most Probable Best
We consider an expected-value ranking and selection problem where all k
solutions' simulation outputs depend on a common uncertain input model. Given
that the uncertainty of the input model is captured by a probability simplex on
a finite support, we define the most probable best (MPB) to be the solution
whose probability of being optimal is the largest. To devise an efficient
sampling algorithm to find the MPB, we first derive a lower bound to the large
deviation rate of the probability of falsely selecting the MPB, then formulate
an optimal computing budget allocation (OCBA) problem to find the optimal
static sampling ratios for all solution-input model pairs that maximize the
lower bound. We devise a series of sequential algorithms that apply
interpretable and computationally efficient sampling rules and prove their
sampling ratios achieve the optimality conditions for the OCBA problem as the
simulation budget increases. The algorithms are benchmarked against a
state-of-the-art sequential sampling algorithm designed for contextual ranking
and selection problems and demonstrated to have superior empirical performances
at finding the MPB