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 language | English |
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Pages (from-to) | 1871-1888 |
Number of pages | 18 |
Journal | Oper Res |
Volume | 71 |
Issue number | 5 |
DOIs | |
State | Published - 1 Sep 2023 |
Keywords
- bias
- coherent measures of risk
- consistency
- kernel estimation
- stochastic programming
- strong law of large numbers
- wavelet estimation