Stability and Sample-based Approximations of Composite Stochastic Optimization Problems

2022/01/04 by Darinka Dentcheva, Yang Lin, Dentcheva, Darinka +3
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Reservoir Engineering and Simulation Methods #Risk and Portfolio Optimization #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2201.01338

openalex publication_date 2022/01/04 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

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.

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