 Constructing unbiased gradient estimators with finite variance for conditional stochastic optimizationTakashi Goda and Wataru Kitade Mathematics and Computers in Simulation (MATCOM), 2023, vol. 204, issue C, 743-763 Abstract: We study stochastic gradient descent for solving conditional stochastic optimization problems, in which an objective to be minimized is given by a parametric nested expectation with an outer expectation taken with respect to one random variable and an inner conditional expectation with respect to the other random variable. The gradient of such a parametric nested expectation is again expressed as a nested expectation, which makes it hard for the standard nested Monte Carlo estimator to be unbiased. In this paper, we show under some conditions that a multilevel Monte Carlo gradient estimator is unbiased and has finite variance and finite expected computational cost, so that the standard theory from stochastic optimization for a parametric (non-nested) expectation directly applies. We also discuss a special case for which yet another unbiased gradient estimator with finite variance and cost can be constructed. Keywords: Conditional stochastic optimization; Nested expectation; Stochastic gradient descent; Multilevel Monte Carlo (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:204:y:2023:i:c:p:743-763 DOI: 10.1016/j.matcom.2022.09.012 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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