英文标题：
《Understanding Distributional Ambiguity via Non-robust Chance Constraint》
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作者：
Qi Wu, Shumin Ma, Cheuk Hang Leung, Wei Liu and Nanbo Peng
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最新提交年份：
2020
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英文摘要：
  This paper provides a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the distributional uncertainties to the chance probabilities. Our analysis allows a decision-maker to interpret the size of the ambiguity set, which is often lack of business meaning, through the chance parameters constraining the objective function. We first show that, for general $\\phi$-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problems. These mean-deviation problems are not subject to uncertain distributions, and the ambiguity radius in the original DRO problem now plays the role of controlling the risk preference of the decision-maker. We then demonstrate that a DRO problem can be cast as a chance-constrained optimization (CCO) problem when a boundedness constraint is added to the decision variables. Without the boundedness constraint, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Thanks to our high-order expansion result, a notable feature of our analysis is that it applies to divergence measures that accommodate well heavy tail distributions such as the student $t$-distribution and the lognormal distribution, besides the widely-used Kullback-Leibler (KL) divergence, which requires the distribution of the objective function to be exponentially bounded. Using the portfolio selection problem as an example, our comprehensive testings on multivariate heavy-tail datasets, both synthetic and real-world, shows that this business-interpretation approach is indeed useful and insightful.
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中文摘要：
本文通过将分布不确定性与机会概率联系起来，给出了分布鲁棒优化（DRO）问题的非鲁棒性解释。我们的分析允许决策者通过约束目标函数的机会参数来解释通常缺乏业务意义的模糊集的大小。我们首先证明，对于一般的$\\φ$-发散，一个DRO问题渐近等价于一类平均偏差问题。这些平均偏差问题不受不确定分布的影响，原始DRO问题中的模糊半径现在起到了控制决策者风险偏好的作用。然后，我们证明了当决策变量中加入有界约束时，DRO问题可以转化为机会约束优化（CCO）问题。在没有有界约束的情况下，无论模糊集的半径、散度度量的选择或中心分布的尾部重量如何，CCO问题的性能都优于DRO问题。由于我们的高阶展开结果，我们分析的一个显著特征是，除了广泛使用的Kullback-Leibler（KL）散度外，它还适用于适应厚尾分布的散度度量，如student$t$-分布和对数正态分布，这要求目标函数的分布为指数有界。以投资组合选择问题为例，我们对多变量重尾数据集（包括合成数据集和真实数据集）的综合测试表明，这种业务解释方法确实有用且富有洞察力。
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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