DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

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Coupled finite-difference simulation-gradient estimator

Definition

Use Simulation objectives and unbiased payoff oracles: let $H : Θ \times Ω \to R$ be the simulation payoff on its probability space and write its objective as $J (η) : = E [H (η, \cdot)] .$ For $θ \in Θ$ , a direction $v \in R^{d}$ , and $h > 0$ with $θ \pm h v \in Θ$ , the coupled central-difference estimator is the random variable $D_{h, v}^{c o u p} (ω) : = \frac{H (θ + h v, ω) - H (θ - h v, ω)}{2 h} .$ The same random input $ω$ is used in both terms; this fixes their joint law and, when both payoffs are square-integrable, their covariance. The estimator's variance is not asserted to be smaller for every coupling.

Depends on

Simulation objectives and unbiased payoff oracles

Used by

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Michael C. Fu, Stochastic Gradient Estimation, preprint of Handbook of Simulation Optimization, §§3.1 and 3.3.4 (standard reference, not scraped)