Root Finding via DARTS: Dynamic Adaptive Random Target Shooting. Pasupathy, R. & Schmeiser, B. W. In B. Johansson, S. Jain, J. Montoya-Torres, J. Hugan, & E. Yücesan, editors, Proceedings of the 2010 Winter Simulation Conference, pages 1255–1262, Piscataway, NJ, 2010. Institute of Electrical and Electronics Engineers, Inc.. Paper abstract bibtex Consider multi-dimensional root finding when the equations are available only implicitly via a Monte Carlo simulation oracle that for any solution returns a vector of point estimates. We develop DARTS, a stochastic-approximation algorithm that makes quasi-Newton moves to a new solution whenever the current sample size is large compared to the estimated quality of the current solution and estimated sampling error. We show that DARTS converges in a certain precise sense, and discuss reasons to expect substantial computational efficiencies over traditional stochastic approximation variations.
@inproceedings{2010passchAWSC,
author = {R. Pasupathy and B. W. Schmeiser},
title = {Root Finding via DARTS: Dynamic Adaptive Random Target Shooting},
booktitle = {Proceedings of the 2010 Winter Simulation Conference},
Publisher = {Institute of Electrical and Electronics Engineers, Inc.},
Address = {Piscataway, NJ},
Editor = {B.~Johansson and S.~Jain and J.~Montoya-Torres and J.~Hugan and E.~Y\"{u}cesan},
pages = {1255--1262},
year = {2010},
url = {http://www.informs-sim.org/wsc10papers/115.pdf},
keywords = {stochastic root-finding, stochastic approximation},
abstract = {Consider multi-dimensional root finding when the equations are available only implicitly via a Monte Carlo simulation oracle that for any solution returns a vector of point estimates. We develop DARTS, a stochastic-approximation algorithm that makes quasi-Newton moves to a new solution whenever the current sample size is large compared to the estimated quality of the current solution and estimated sampling error. We show that DARTS converges in a certain precise sense, and discuss reasons to expect substantial computational efficiencies over traditional stochastic approximation variations.}}
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