Stability and Sample-Based Approximations of Composite Stochastic Optimization Problems

Optimization under uncertainty and risk is ubiquitous in business, engineering, finance. Typically, we use observed or simulated data our decision models, which aim to control risk, result composite functionals. The paper addresses the stability of problems when functionals are subjected measure perturbations at multiple levels potentially different nature. We analyze data-driven formulations with empirical smoothing estimators such as kernels wavelets applied some all functions compositions establish laws large numbers consistency optimal values solutions. This first study propose optimization problems. It shown that kernel-based wavelet estimation provide less biased compared plug-in assumptions.