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.

翻译：在许多实际情况下,在不确定和风险情况下,优化是不可或缺的。我们的文件用综合风险功能处理优化问题的稳定性问题,这些功能会受到测量干扰。我们的主要焦点是数据驱动的配方的无症状行为,这些配方有经验性或平滑的估测器,如适用于组成的某些或所有功能的内核或波子。我们分析新估测器的特性,并在相当一般的假设下制定大量、一致和减少偏差潜力的强有力法律。我们的结果与风险反优化和一般数据科学密切相关。