research-article

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

Authors:

Jose H. Blanchet,

Peter W. GlynnAuthors Info & Claims

WSC '15: Proceedings of the 2015 Winter Simulation Conference

Pages 3656 - 3667

Published: 06 December 2015 Publication History

Abstract

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.

References

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Asmussen, S. 2000. Applied Probability and Queues (2nd. Ed.). Springer-Verlag, New York.

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Asmussen, S., and P. Glynn. 2008. Stochastic Simulation: Algorithms and Analysis. New York, NY, USA: Springer-Verlag.

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Blanchet, J. H., N. Chen, and P. W. Glynn. 2015. "Unbiased Monte Carlo Computation of Smooth Functions of Expectations via Taylor Expansions". In Proceedings of the 2015 Winter Simulation Conference, edited by L. Yilmaz, W. K. V. Chan, I. Moon, T. M. K. Roeder, C. Macal, and M. D. Rossetti, To appear.

Digital Library

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Blanchet, J. H., and P. W. Glynn. 2015. "Unbiased Monte Carlo Computations for Optimization and Functions of Expectations". In progress.

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Bujok, K., B. Hambly, and C. Reisinger. 2013. "Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives". Methodology and Computing in Applied Probability.

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Rhee, C., and P. W. Glynn. 2011. "A New Approach to Unbiased Estimation for SDE's". In Proceedings of the 2011 Winter Simulation Conference, edited by C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher, 495--503.

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Rhee, C., and P. W. Glynn. 2015. "Unbiased Estimation with Square Root Convergence for SDE Models". To appear in Operations Research.

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Cited By

Wang YVelasquez AAtia GPrater-Bennette AZou SKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Model-free robust average-reward reinforcement learningProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619924(36431-36469)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619924
Syed YWang GKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Optimal randomized multilevel Monte Carlo for repeatedly nested expectationsProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619795(33343-33364)Online publication date: 23-Jul-2023
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Carmon YHausler DKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Distributionally robust optimization via ball oracle accelerationProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602869(35866-35879)Online publication date: 28-Nov-2022
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Unbiased Monte Carlo for optimization and functions of expectations via multi-level randomization
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cover image ACM Conferences

WSC '15: Proceedings of the 2015 Winter Simulation Conference

December 2015

4051 pages

ISBN:9781467397414

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SIGSIM: ACM Special Interest Group on Simulation and Modeling

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IEEE Press

Publication History

Published: 06 December 2015

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WSC '15

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SIGSIM

WSC '15: Winter Simulation Conference

December 6 - 9, 2015

California, Huntington Beach

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WSC '15 Paper Acceptance Rate 202 of 296 submissions, 68%;

Overall Acceptance Rate 3,285 of 4,888 submissions, 67%

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Cited By

Wang YVelasquez AAtia GPrater-Bennette AZou SKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Model-free robust average-reward reinforcement learningProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619924(36431-36469)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619924
Syed YWang GKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Optimal randomized multilevel Monte Carlo for repeatedly nested expectationsProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619795(33343-33364)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619795
Carmon YHausler DKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Distributionally robust optimization via ball oracle accelerationProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3602869(35866-35879)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3602869
Ghosh SSquillante MWollega E(2021)On solving distributionally robust optimization formulations efficientlyProceedings of the Winter Simulation Conference10.5555/3522802.3523019(1-12)Online publication date: 13-Dec-2021
https://dl.acm.org/doi/10.5555/3522802.3523019
Levy DCarmon YDuchi JSidford ALarochelle HRanzato MHadsell RBalcan MLin H(2020)Large-scale methods for distributionally robust optimizationProceedings of the 34th International Conference on Neural Information Processing Systems10.5555/3495724.3496466(8847-8860)Online publication date: 6-Dec-2020
https://dl.acm.org/doi/10.5555/3495724.3496466
Moka SKroese DJuneja SSon YHaas P(2019)Unbiased estimation of the reciprocal mean for non-negative random variablesProceedings of the Winter Simulation Conference10.5555/3400397.3400430(404-415)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3400397.3400430
Giles MGoda T(2019)Decision-making under uncertaintyStatistics and Computing10.1007/s11222-018-9835-129:4(739-751)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s11222-018-9835-1
Duplay TLam HZhang XJohansson BJain S(2018)Achieving optimal bias-variance tradeoff in online derivative estimationProceedings of the 2018 Winter Simulation Conference10.5555/3320516.3320739(1838-1849)Online publication date: 9-Dec-2018
https://dl.acm.org/doi/10.5555/3320516.3320739
Glynn PHuschka TChick S(2016)Exact simulation vs exact estimationProceedings of the 2016 Winter Simulation Conference10.5555/3042094.3042130(193-205)Online publication date: 11-Dec-2016
https://dl.acm.org/doi/10.5555/3042094.3042130
Blanchet JChen NGlynn P(2015)Unbiased monte carlo computation of smooth functions of expectations via Taylor expansionsProceedings of the 2015 Winter Simulation Conference10.5555/2888619.2888658(360-367)Online publication date: 6-Dec-2015
https://dl.acm.org/doi/10.5555/2888619.2888658

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