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Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We consider the context of \u201csimulation-based recursions,\u201d that is, recursions that involve quantities needing to be estimated using a stochastic simulation. Examples include stochastic adaptations of fixed-point and gradient descent recursions obtained by replacing function and derivative values appearing within the recursion by their Monte Carlo counterparts. The primary motivating settings are simulation optimization and stochastic root finding problems, where the low point and the zero of a function are sought, respectively, with only Monte Carlo estimates of the functions appearing within the problem. We ask how much Monte Carlo sampling needs to be performed within simulation-based recursions in order that the resulting iterates remain consistent and, more importantly, efficient, where \u201cefficient\u201d implies convergence at the fastest possible rate. Answering these questions involves trading off two types of error inherent in the iterates: the deterministic error due to recursion and the \u201cstochastic\u201d error due to sampling. As we demonstrate through a characterization of the relationship between sample sizing and convergence rates, efficiency and consistency are intimately coupled with the speed of the underlying recursion, with faster recursions yielding a wider regime of \u201coptimal\u201d sampling rates. The implications of our results for practical implementation are immediate since they provide specific guidance on optimal simulation expenditure within a variety of stochastic recursions.<\/jats:p>","DOI":"10.1137\/140951679","type":"journal-article","created":{"date-parts":[[2018,1,9]],"date-time":"2018-01-09T12:22:12Z","timestamp":1515500532000},"page":"45-73","source":"Crossref","is-referenced-by-count":34,"title":["On Sampling Rates in Simulation-Based Recursions"],"prefix":"10.1137","volume":"28","author":[{"given":"Raghu","family":"Pasupathy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Glynn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Soumyadip","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fatemeh S.","family":"Hashemi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,9]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"O. Alagoz, A. J. Schaefer, and M. S. Roberts,\n                      Optimization in organ allocation\n                      , in Handbook of Optimization in Medicine, P. Pardalos and E. Romeijn, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2009.","DOI":"10.1007\/978-0-387-09770-1_1"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"S. Asmussen and P. W. Glynn,\n                      Stochastic Simulation: Algorithms and Analysis\n                      , Springer, New York, 2007.","DOI":"10.1007\/978-0-387-69033-9"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1070.0774"},{"key":"atypb4","unstructured":"D. Bertsekas,\n                      Nonlinear Programming\n                      , Athena Scientific, Nashua, NH, 1995."},{"key":"atypb5","unstructured":"P. Billingsley,\n                      Probability and Measure\n                      , Wiley, New York, 1995."},{"key":"atypb6","unstructured":"V. S. Borkar,\n                      Stochastic Approximation: A Dynamical Systems Viewpoint\n                      , Cambridge University Press, Cambridge, UK, 2008."},{"key":"atypb7","first-page":"161","author":"Bottou L.","year":"2008","journal-title":"NY"},{"key":"atypb8","unstructured":"L. Bottou, F. Curtis, and J. Nocedal,\n                      Optimization methods for large-scale machine learning\n                      , preprint,https:\/\/arxiv.org\/abs\/1606.04838, 2016."},{"key":"atypb9","unstructured":"S. Boyd,\n                      Convex Optimization\n                      , Cambridge University Press, Cambridge, UK, 2004."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0572-5"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/50\/23\/003"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"A. R. Conn, K. Scheinberg, and L. N. Vicente,\n                      Introduction to Derivative-Free Optimization\n                      , MOS-SIAM Ser. Optim. 8, SIAM, Philadelphia, 2009,https:\/\/doi.org\/10.1137\/1.9780898718768.","DOI":"10.1137\/1.9780898718768"},{"key":"atypb13","first-page":"312","author":"Deng G.","year":"2006","journal-title":"NJ"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1038\/nature02541"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/110830629"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/120880811"},{"key":"atypb17","unstructured":"S. G. Henderson and B. L. Nelson, eds.\n                      Handbooks in Operations Research and Management Science: Simulation\n                      , vol. 13, Elsevier, New York, 2006."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1080\/07408170500434539"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.45.1.86"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729392"},{"key":"atypb21","unstructured":"A. M. Law,\n                      Simulation Modeling and Analysis\n                      , McGraw-Hill, New York, 2007."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/070704277"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"Y. Nesterov,\n                      Introductory Lectures on Convex Optimization: A Basic Course\n                      , Springer, New York, 2004.","DOI":"10.1007\/978-1-4419-8853-9"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2013.1226"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1090.0773"},{"key":"atypb26","first-page":"122","author":"Pasupathy R.","year":"2013","journal-title":"MD"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"R. Pasupathy and S. Kim,\n                      The stochastic root-finding problem: Overview, solutions, and open questions\n                      , ACM TOMACS, 21(3), 2011.","DOI":"10.1145\/1921598.1921603"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1145\/1502787.1502788"},{"key":"atypb29","unstructured":"R. Pasupathy and B. W. Schmeiser,\n                      DARTS-dynamic adaptive random target shooting\n                      , in Proceedings of the 2010 Winter Simulation Conference, B. Johansson, S. Jain, J. Montoya-Torres, J. Hugan, and E. Yu\u0308cesan, eds., IEEE, Piscataway, NJ, 2010."},{"key":"atypb30","unstructured":"B. Polyak,\n                      Introduction to Optimization\n                      , Optimization Software, New York, NY, 1987."},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/0330046"},{"key":"atypb32","doi-asserted-by":"crossref","unstructured":"R. J. 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