Unbiased Monte Carlo for Optimization and Functions of Expectations via Multilevel RandomizationJ. Blanchet and P. W. Glynn Proceedings of the Winter Simulation Conference (2015) pp.3656-3667. We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as alpha = 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. |