论文标题
有效的嵌套模拟实验设计通过似的比率法
Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method
论文作者
论文摘要
在嵌套的仿真文献中，一个共同的假设是实验者可以选择要采样的外部情况的数量。本文考虑了从外部实体赋予实验者固定的外部情况的情况。我们提出了一个嵌套的仿真实验设计，该设计从一个方案中汇集了内部复制，以通过似然比方法估算另一种情况的条件平均值。在外部情况下，我们决定在每个外部情况下运行多少个内部复制，以及如何通过解决双层优化问题来汇总内部复制，从而最大程度地减少了总模拟工作。我们对根据优化实验设计计算的性能度量估计量的收敛速率进行渐近分析。在某些假设下，优化的设计实现了$ \ co（γ^{ - 1}）$的平方误差，给定模拟预算$γ$的估计器。数值实验表明，我们的设计优于最先进的设计，该设计通过回归汇总复制。
In nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario's conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bi-level optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves $\cO(Γ^{-1})$ mean squared error of the estimators given simulation budget $Γ$. Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression.
