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.

本研究解决了在不确定性条件下决策问题的挑战，尤其是当概率分布本身存在不确定性时。文章提出了一种新的方法，强调模糊集合在最坏情况下选择决策的重要性，并展示了心理学和神经科学的支持。研究的主要发现是，分布鲁棒优化与机器学习中的正则化技术和对抗训练之间存在深刻联系，具有重要的应用潜力。