GETTING TO “RATE-OPTIMAL” IN RANKING & SELECTION
GETTING TO “RATE-OPTIMAL” IN RANKING & SELECTION
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发表时间：
2021
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通讯作者：
B. Feng;K. Smith;S. Masoud;Z. Zheng;C. Szabó;M. Loper
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作者：
B. Feng;K. Smith;S. Masoud;Z. Zheng;C. Szabó;M. Loper
在他们2004年的开创性论文中，Glynn和Juneja正式而精确地建立了从k个模拟系统中选择最佳系统的速率最优、错误选择概率和复制分配方案。在独立的、正态分布的输出的情况下，这种分配有一个简单的形式，以一种直观的吸引人的方式依赖于真实的均值和方差。当然，平均值和（通常）方差是未知的，但是速率最优分配为可实现的、动态的、数据驱动的策略提供了一个目标。本文比较了四种相关的复制-分配策略的实证行为：Chen和Rzyhov的mCEI和我们的新gCEI策略都收敛于Glynn和Juneja分配；收敛于OCBA最优配置的来自Peng和Fu的AOMAP；以及Russo的TTTS，其目标是错误选择的后验概率的收敛速度。我们发现这些策略在某些设置中具有明显不同的行为。
In their 2004 seminal paper, Glynn and Juneja formally and precisely established the rate-optimal, probability-of-incorrect-selection, replication allocation scheme for selecting the best of k simulated systems. In the case of independent, normally distributed outputs this allocation has a simple form that depends in an intuitively appealing way on the true means and variances. Of course the means and (typically) variances are unknown, but the rate-optimal allocation provides a target for implementable, dynamic, data-driven policies to achieve. In this paper we compare the empirical behavior of four related replication-allocation policies: mCEI from Chen and Rzyhov and our new gCEI policy that both converge to the Glynn and Juneja allocation; AOMAP from Peng and Fu that converges to the OCBA optimal allocation; and TTTS from Russo that targets the rate of convergence of the posterior probability of incorrect selection. We find that these policies have distinctly different behavior in some settings.