英文标题：
《Calibration of Distributionally Robust Empirical Optimization Models》
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作者：
Jun-Ya Gotoh, Michael Jong Kim, Andrew E.B. Lim
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最新提交年份：
2020
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英文摘要：
  We study the out-of-sample properties of robust empirical optimization problems with smooth $\\phi$-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative \"robustness parameter\" $\\delta$ that controls the size of the deviations from the nominal model. Building on the intuition that robust optimization reduces the sensitivity of the expected reward to errors in the model by controlling the spread of the reward distribution, we show that the first-order benefit of ``little bit of robustness\" (i.e., $\\delta$ small, positive) is a significant reduction in the variance of the out-of-sample reward while the corresponding impact on the mean is almost an order of magnitude smaller. One implication is that substantial variance (sensitivity) reduction is possible at little cost if the robustness parameter is properly calibrated. To this end, we introduce the notion of a robust mean-variance frontier to select the robustness parameter and show that it can be approximated using resampling methods like the bootstrap. Our examples show that robust solutions resulting from \"open loop\" calibration methods (e.g., selecting a $90\\%$ confidence level regardless of the data and objective function) can be very conservative out-of-sample, while those corresponding to the robustness parameter that optimizes an estimate of the out-of-sample expected reward (e.g., via the bootstrap) with no regard for the variance are often insufficiently robust.
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中文摘要：
我们研究了具有光滑$\\ phi$-散度惩罚和光滑凹目标函数的稳健经验优化问题的样本外性质，并发展了一种数据驱动的非负“稳健参数”$\\ delta$校准理论，该参数控制与标称模型的偏差大小。基于鲁棒优化通过控制奖励分布的扩散来降低预期奖励对模型中错误的敏感性的直觉，我们表明，“小一点稳健性”（即$\\ delta$小，正）的一阶好处是显著减少样本外奖励的方差，而对平均值的相应影响几乎小一个数量级。一个含义是显著的方差（敏感性）如果稳健性参数得到适当校准，则可以以较小的成本降低。为此，我们引入了稳健均值-方差边界的概念来选择稳健参数，并表明可以使用重采样方法（如bootstrap）来逼近稳健参数。我们的示例表明，“开环”校准方法（例如，无论数据和目标函数如何，选择90美元\\%$置信水平）产生的稳健解决方案在样本外可能非常保守，而那些与稳健性参数相对应的参数（例如，通过bootstrap）在不考虑方差的情况下优化样本外预期回报的估计值，通常稳健性不足。
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分类信息：

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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一级分类：Computer Science        计算机科学
二级分类：Systems and Control        系统与控制
分类描述：cs.SY is an alias for eess.SY. This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
cs.sy是eess.sy的别名。本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Systems and Control        系统与控制
分类描述：This section includes theoretical and experimental research covering all facets of automatic control systems. The section is focused on methods of control system analysis and design using tools of modeling, simulation and optimization. Specific areas of research include nonlinear, distributed, adaptive, stochastic and robust control in addition to hybrid and discrete event systems. Application areas include automotive and aerospace control systems, network control, biological systems, multiagent and cooperative control, robotics, reinforcement learning, sensor networks, control of cyber-physical and energy-related systems, and control of computing systems.
本部分包括理论和实验研究，涵盖了自动控制系统的各个方面。本节主要介绍利用建模、仿真和优化工具进行控制系统分析和设计的方法。具体研究领域包括非线性、分布式、自适应、随机和鲁棒控制，以及混合和离散事件系统。应用领域包括汽车和航空航天控制系统、网络控制、生物系统、多智能体和协作控制、机器人学、强化学习、传感器网络、信息物理和能源相关系统的控制以及计算系统的控制。
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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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