Classical supervised learning via empirical risk (or negative log-likelihood) minimization hinges upon the assumption that the testing distribution coincides with the training distribution. This assumption can be challenged in modern applications of machine learning in which learning machines may operate at prediction time with testing data whose distribution departs from the one of the training data. We revisit the superquantile regression method by proposing a first-order optimization algorithm to minimize a superquantile-based learning objective. The proposed algorithm is based on smoothing the superquantile function by infimal convolution. Promising numerical results illustrate the interest of the approach towards safer supervised learning.
Fast Computation of Superquantile-Constrained Optimization Through Implicit Scenario Reduction
Department of Industrial and Systems Engineering, University of Minnesota（明尼苏达大学工业与系统工程系）；Department of Industrial Engineering and Operations Research, University of California, Berkeley（加州大学伯克利分校工业工程与运筹学系）
Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density Estimation
条件风险价值（CVaR）和风险价值（VaR），也被称为超分位数和分位数，经常被用来描述概率分布的尾部，是流行的风险度量。缓冲超额概率（Buffered Probability of Exceedance，bPOE）是最近引入的尾部特征，它是CVaR的倒数，就像CDF是分位数的倒数一样。这些数量可以证明是非常有用的各种风险规避参数工程方法的基础。然而，它们的使用往往是困难的，因为缺乏众所周知的封闭式方程来计算这些常用的概率分布的数量。在本文中，我们推导出了各种常见的一元概率分布的超分位数和bPOE的公式。除了提供一个有用的集合在一个单一的参考，我们使用这些公式将超分位数和bPOE参数化的过程。特别地，我们考虑两个：投资组合优化和密度估计。首先，当投资组合收益率假设遵循特定的分布家庭，我们发现，通过最小化bPOE的最优投资组合具有优势，超分位数最小化。我们表明，给定一个固定的阈值，一个单一的投资组合是最小的bPOE投资组合的整个类的分布的同时。其次，我们将我们的公式应用于参数密度估计，并提出了超分位数的方法（MOS），一个简单的变化的矩的方法（MM），其中时刻的取代超分位数的在不同的置信水平。由于可以自由选择置信水平的各种组合，MOS允许用户将拟合过程集中在分布的不同部分，例如拟合重尾非对称数据时的尾部。
PPI-SVRG: Unifying Prediction-Powered Inference and Variance Reduction for Semi-Supervised Optimization
Institute for Data, Systems, and Society（数据、系统与社会研究所）；Massachusetts Institute of Technology（麻省理工学院）；Department of Mathematics（数学系）；Washington University in Saint Louis（圣路易斯华盛顿大学）；Daniels School of Business（丹尼尔斯商学院）
A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Hong Kong Baptist University（香港浸会大学）；Sun Yat-sen University（中山大学）
Control and optimization for Neural Partial Differential Equations in Supervised Learning
Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, TX 75080, USA；Department of Mathematics, Texas A\&M University, College Station, TX 77843, USA
Offline Supervised Learning V.S. Online Direct Policy Optimization: A Comparative Study and A Unified Training Paradigm for Neural Network-Based Optimal Feedback Control
Center for Data Science, Peking University（北京大学数据科学中心）；Flatiron Institute（弗拉蒂伦研究所）
Non-convergence to global minimizers in data driven supervised deep learning: Adam and stochastic gradient descent optimization provably fail to converge to global minimizers in the training of deep neural networks with ReLU activation
School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）；Vietnam Academy of Science and Technology（越南科学技术研究院）；Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）深圳大数据研究院）
Combining Trajectory Optimization, Supervised Machine Learning, and Model Structure for Mitigating the Curse of Dimensionality in the Control of Bipedal Robots
