Stability and Sample-Based Approximations of Composite Stochastic Optimization Problems

Darinka Dentcheva, Yang Lin, Spiridon Penev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)1871-1888
Number of pages18
JournalOper Res
Volume71
Issue number5
DOIs
StatePublished - 1 Sep 2023

Keywords

  • bias
  • coherent measures of risk
  • consistency
  • kernel estimation
  • stochastic programming
  • strong law of large numbers
  • wavelet estimation

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