We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem (which is also known as the empirical risk minimization (ERM) rule in learning literature). It is well known that for some simple stochastic optimization problems, the sample average estimator may not be admissible. This is known as {\em Stein's paradox} in the statistics literature. We show in this paper that for optimizing stochastic linear functions over compact sets, the sample average estimator is admissible. Moreover, we study problems with convex quadratic objectives subject to box constraints. Stein's paradox holds when there are no constraints and the dimension of the problem is at least three. We show that in the presence of box constraints, admissibility is recovered for dimensions 3 and 4.
估计再生核希尔伯特空间（RKHS）中的核均值的问题是核方法的核心，因为它被经典方法（例如，当将核PCA矩阵居中时），并且它还形成现代核方法的核心推理步骤（例如，基于核的非参数检验），其依赖于在RKHS中嵌入概率分布。Muandet等人（2014）已经表明，收缩可以帮助构建比经验估计量“更好”的核均值估计量。本文研究了Muandet et al.（2014）中估计量的相容性和可容许性，并提出了一类更广泛的收缩估计量，通过考虑适当的基函数来改进经验估计量。使用核PCA的基础上，我们表明，这些估计可以使用频谱滤波算法，这是一致的，在一些技术假设。我们的理论分析还揭示了与基于内核的监督学习框架的基本联系。建议的估计是简单的实现和执行良好的实践。
Explicit construction of the minimum error variance estimator for stochastic LTI state-space systems
Dept. of Electronic Systems, Aalborg University, Aalborg, Denmark（丹麦奥尔堡大学电子系统系）；Laboratoire Signal et Automatique de Lille (CRIStAL), Lille, France（法国里尔信号与自动化实验室（CRIStAL））
Zeroth-Order Gradient Estimators under Decision-Dependent Noise
Graduate School of Information Science and Technology, University of Tokyo（东京大学信息理工学系研究科）；Center for Advanced Intelligence Project, RIKEN（理化学研究所先进智能项目中心）
Sharp bounds for stochastic proximal and projection estimators via radial dominance
Universidad Técnica Federico Santa María（费德里科·圣塔玛丽亚技术大学）；Center for Mathematical Modeling (CNRS IRL2807), Universidad de Chile（智利大学数学建模中心（法国国家科学研究中心国际研究联系项目2807））；Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins（奥希金斯大学工程科学学院）
Convergence Rates for Stochastic Proximal and Projection Estimators
Universidad de Chile（智利大学）；Center for Mathematical Modeling (CMM), Universidad de Chile（智利大学数学建模中心）；Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins（奥希金斯大学工程科学研究所）
Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusions
Department of Statistics and Operations Research（统计与运筹学系）；The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Hanes Hall, UNC-Chapel Hill, NC 27599-3260（UNC-教堂山分校318号哈尼斯楼，NC 27599-3260）
