Stability and Sample-Based Approximations of Composite Stochastic Optimization Problems

Darinka Dentcheva, Yang Lin () and Spiridon Penev ()
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Yang Lin: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 03070
Spiridon Penev: School of Mathematics and Statistics and University of New South Wales Data Science Hub, University of New South Wales, Sydney, 2052 New South Wales, Australia

Operations Research, 2023, vol. 71, issue 5, 1871-1888

Abstract: Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals that are subjected to multiple 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.

Keywords: Optimization; stochastic programming; bias; coherent measures of risk; kernel estimation; wavelet estimation; consistency; strong law of large numbers (search for similar items in EconPapers)
Date: 2023
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