We study a ranking and selection (R&S) problem when all solutions share common parametric Bayesian input models updated with the data collected from multiple independent data-generating sources. Our objective is to identify the best system by designing a sequential sampling algorithm that collects input and simulation data given a budget. We adopt the most probable best (MPB) as the estimator of the optimum and show that its posterior probability of optimality converges to one at an exponential rate as the sampling budget increases. Assuming that the input parameters belong to a finite set, we characterize the $\epsilon$-optimal static sampling ratios for input and simulation data that maximize the convergence rate. Using these ratios as guidance, we propose the optimal sampling algorithm for R&S (OSAR) that achieves the $\epsilon$-optimal ratios almost surely in the limit. We further extend OSAR by adopting the kernel ridge regression to improve the simulation output mean prediction. This not only improves OSAR's finite-sample performance, but also lets us tackle the case where the input parameters lie in a continuous space with a strong consistency guarantee for finding the optimum. We numerically demonstrate that OSAR outperforms a state-of-the-art competitor.

翻译：本文研究了一个排序与选择（R&S）问题，其中所有备选方案共享共同的参数化贝叶斯输入模型，这些模型通过从多个独立数据生成源收集的数据进行更新。我们的目标是通过设计一种序贯采样算法，在给定预算条件下收集输入数据和仿真数据，从而识别最优系统。我们采用最可能最优（MPB）作为最优解的估计量，并证明随着采样预算的增加，其最优性的后验概率以指数速率收敛到一。假设输入参数属于有限集合，我们刻画了输入数据与仿真数据的$\epsilon$最优静态采样比例，该比例能最大化收敛速率。以此比例为指引，我们提出了用于R&S的最优采样算法（OSAR），该算法在极限情况下几乎必然达到$\epsilon$最优比例。我们进一步通过采用核岭回归来改进仿真输出均值预测，从而扩展了OSAR。这不仅提升了OSAR在有限样本下的性能，还使我们能够处理输入参数位于连续空间的情况，并为寻找最优解提供了强一致性保证。数值实验表明，OSAR优于当前最先进的竞争方法。