Given a fixed simulation budget, the problem of selecting the best and top- alternatives among a finite set of alternatives have been studied separately in simulation optimization literature, because the existing sampling procedures are often dedicated to one problem. Under a Bayesian framework, we formulate the top- selection into a stochastic dynamic program, and characterize the optimal sampling policy via Bellman equations. To determine sequential sampling decisions, we measure the expected marginal improvement from obtaining one additional simulation observation based on predictive distributions, and then develop two cheaply computational approximations to the improvement, thereby yielding two generic sampling procedures that are efficient in selecting top- alternative(s). The two procedures are proved to be consistent, in a sense that the best and top- alternatives can be correctly identified as the simulation budget goes to infinity. Numerical experiments on synthetic problems and a coronavirus transmission control application are conducted to demonstrate the efficiency and generality of our procedures.

中文翻译：

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顶级[公式省略]选择的边际改进程序


给定固定的模拟预算，在模拟优化文献中已经单独研究了在有限的一组替代方案中选择最佳和顶级替代方案的问题，因为现有的采样程序通常专用于一个问题。在贝叶斯框架下，我们将最优选择制定为随机动态程序，并通过贝尔曼方程描述最优采样策略。为了确定顺序抽样决策，我们根据预测分布获得一项额外的模拟观察来测量预期的边际改进，然后开发两种廉价的改进计算近似值，从而产生两个通用抽样程序，它们可以有效地选择最佳替代方案）。这两个过程被证明是一致的，从某种意义上说，当模拟预算趋于无穷大时，可以正确识别最佳和最佳替代方案。对合成问题和冠状病毒传播控制应用进行了数值实验，以证明我们程序的效率和通用性。