We investigate the merits of replication, and provide methods for optimal
design (including replicates), with the goal of obtaining globally accurate
emulation of noisy computer simulation experiments. We first show that
replication can be beneficial from both design and computational perspectives,
in the context of Gaussian process surrogate modeling. We then develop a
lookahead based sequential design scheme that can determine if a new run should
be at an existing input location (i.e., replicate) or at a new one (explore).
When paired with a newly developed heteroskedastic Gaussian process model, our
dynamic design scheme facilitates learning of signal and noise relationships
which can vary throughout the input space. We show that it does so efficiently,
on both computational and statistical grounds. In addition to illustrative
synthetic examples, we demonstrate performance on two challenging real-data
simulation experiments, from inventory management and epidemiology.

本文研究了复制的优点并提供了最优设计方法，使用高斯过程代理模型获得全局准确性噪声计算机模拟实验的模拟。利用新开发的异方差高斯过程模型实现了动态设计方案，使其在计算和统计方面都有效，展示了其在库存管理和流行病学等两个挑战性的真实数据模拟实验中的性能。

随机模拟实验的顺序设计：复制还是探索？

Replication or exploration? Sequential design for stochastic simulation  experiments

In this paper, we combine ideas from machine learning (ML) and operations
research and management science (OR/MS) in developing a framework, along with
specific methods, for using data to prescribe optimal decisions in OR/MS
problems. In a departure from other work on data-driven optimization and
reflecting our practical experience with the data available in applications of
OR/MS, we consider data consisting, not only of observations of quantities with
direct effect on costs/revenues, such as demand or returns, but predominantly
of observations of associated auxiliary quantities. The main problem of
interest is a conditional stochastic optimization problem, given imperfect
observations, where the joint probability distributions that specify the
problem are unknown. We demonstrate that our proposed solution methods, which
are inspired by ML methods such as local regression, CART, and random forests,
are generally applicable to a wide range of decision problems. We prove that
they are tractable and asymptotically optimal even when data is not iid and may
be censored. We extend this to the case where decision variables may directly
affect uncertainty in unknown ways, such as pricing's effect on demand. As an
analogue to R^2, we develop a metric P termed the coefficient of
prescriptiveness to measure the prescriptive content of data and the efficacy
of a policy from an operations perspective. To demonstrate the power of our
approach in a real-world setting we study an inventory management problem faced
by the distribution arm of an international media conglomerate, which ships an
average of 1bil units per year. We leverage internal data and public online
data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational
decisions that outperform baseline measures. Specifically, the data we collect,
leveraged by our methods, accounts for an 88\% improvement as measured by our
P.

该论文结合了机器学习和运筹学的想法，提出了一种基于数据的最优决策框架和方法，应用于条件随机优化问题中，证明了该方法的实用性和广泛适用性，并通过一个库存管理问题的实际案例展示了该方法的优越性。