Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavor can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parameterized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

翻译：“如何最优地获取数据”这一问题是自然科学、社会科学、工程应用及其他领域建模与预测的核心。最优实验设计（Optimal experimental design, OED）将这些问题形式化，并创建计算方法来回答它们。本文对现代最优实验设计进行了系统综述，涵盖从经典设计理论的基础到涉及复杂模型的当前研究。我们首先回顾用于阐述OED问题并由此编码实验目标的准则。我们强调贝叶斯与决策理论方法的灵活性，该方法包含了适用于非线性及非高斯统计模型的信息型准则。随后，我们讨论估计或约束这些设计准则值的方法；由于强非线性、高参数维度、大样本代价或模型为隐式的情形，此项工作可能极具挑战性。另一组互补的计算问题涉及用于寻找设计的优化方法；我们在观测选择的离散（组合）设定以及精确设计可连续参数化的设定中讨论了此类方法。最后，我们介绍了构建非短视设计策略而非显式设计的序贯OED新兴方法；这些方法能自然地根据过去实验的结果调整以提出新实验，同时寻求所有待执行实验间的协调。在全文过程中，我们强调了重要的开放问题与挑战。