Unbiased Monte Carlo for optimization and functions of expectations via multi-level randomization

We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as α = g(E (X)), where E (X) denotes the expectation of a (possibly multidimensional) random variable X, and g(·) is a given deterministic function. Our estimators possess finite work-nor...

Full description

Saved in:
Bibliographic Details
Main Authors: Blanchet, Jose H., Glynn, Peter W.
Format: Conference Proceeding
Language:English
Subjects:
Approximation
Computer simulation
Conferences
Context
Convergence
Estimation
Estimators
Mathematical analysis
Monte Carlo methods
Optimization
Random variables
Randomization
Xenon
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as α = g(E (X)), where E (X) denotes the expectation of a (possibly multidimensional) random variable X, and g(·) is a given deterministic function. Our estimators possess finite work-normalized variance under mild regularity conditions such as local twice differentiability of g(·) and suitable growth and finite-moment assumptions. We apply our estimator to various settings of interest, such as optimal value estimation in the context of Sample Average Approximations, and unbiased steady-state simulation of regenerative processes. Other applications include unbiased estimators for particle filters and conditional expectations.
ISSN:1558-4305
DOI:10.1109/WSC.2015.7408524