Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the worst distribution in the ambiguity set. This worst case criterion is supported by findings in psychology and neuroscience, which indicate that many decision-makers have a low tolerance for distributional ambiguity. DRO is rooted in statistics, operations research and control theory, and recent research has uncovered its deep connections to regularization techniques and adversarial training in machine learning. This survey presents the key findings of the field in a unified and self-contained manner.

翻译：分布鲁棒优化（DRO）研究不确定条件下的决策问题，其中控制不确定问题参数的概率分布本身也是不确定的。任何DRO模型的一个关键组成部分是其模糊集，即一个与任何可用的结构或统计信息相一致的概率分布族。DRO寻求在模糊集中的最差分布下表现最佳的决策。这种最坏情况准则得到了心理学和神经科学发现的支撑，这些发现表明许多决策者对分布模糊性的容忍度较低。DRO植根于统计学、运筹学和控制理论，最近的研究揭示了其与机器学习中正则化技术和对抗训练的深刻联系。本综述以统一且自包含的方式呈现了该领域的关键发现。