教机器在不确定中做出稳健决策，防止单一分布出错
Distributionally Robust Optimization
- 用模糊集约束可能的分布，选最坏情况下的最优解
- 理论源自统计与控制，近年连接机器学习正则化与对抗训练
- 适合关注鲁棒性、风险控制的研究者
分布鲁棒优化（DRO）研究在不确定性下进行决策的问题，其中决定问题参数的概率分布本身也是不确定的。任何DRO模型的关键组成部分是其模糊集，即与现有结构或统计信息一致的概率分布族。DRO旨在寻找在模糊集中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持，表明许多决策者对分布模糊性容忍度较低。DRO源于统计学、运筹学和控制论，近期研究揭示了其与机器学习中正则化技术和对抗训练的深层联系。本综述以统一且自洽的方式呈现该领域的关键成果。
原文摘要 · Abstract (English)
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.
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