论文标题
复合随机优化问题的稳定性和基于样本的近似值
Stability and Sample-based Approximations of Composite Stochastic Optimization Problems
论文作者
论文摘要
在许多实际情况下，在不确定性和风险下的优化是必不可少的。我们的论文解决了使用复合风险功能的优化问题的稳定性，这些功能受到测量扰动。我们的主要重点是数据驱动的制剂的渐近行为，其经验或平滑估计器（例如核或小波）应用于某些或所有功能。我们分析了新估计器的性质，并在相当普遍的假设下建立了强大的法律，一致性和降低偏差潜力。我们的结果对规避风险的优化和一般数据科学是密切的。
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is the asymptotic behavior of data-driven formulations with empirical or smoothing estimators such as kernels or wavelets applied to some or to all functions of the compositions. We analyze the properties of the new estimators and we establish strong law of large numbers, consistency, and bias reduction potential under fairly general assumptions. Our results are germane to risk-averse optimization and to data science in general.
