Enhanced Balancing of Bias-Variance Tradeoff in Stochastic Estimation: A Minimax Perspective

Published Online:https://doi.org/10.1287/opre.2022.2319

References

  • Agrawal S, Ding Y, Saberi A, Ye Y (2012) Price of correlations in stochastic optimization. Oper. Res. 60(1):150–162.LinkGoogle Scholar
  • Asmussen S, Glynn PW (2007) Stochastic Simulation: Algorithms and Analysis (Springer Science & Business Media, New York).CrossrefGoogle Scholar
  • Barton RR (2012) Input uncertainty in outout analysis. Proceedings of the 2012 Winter Simulation Conference (Institute of Electrical and Electronics Engineers, Washington, DC).Google Scholar
  • Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Ben-Tal A, Nemirovski A (2002) Robust optimization–methodology and applications. Math. Program. 92(3):453–480.CrossrefGoogle Scholar
  • Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.CrossrefGoogle Scholar
  • Besbes O, Zeevi A (2009) Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Oper. Res. 57(6):1407–1420.LinkGoogle Scholar
  • Besbes O, Zeevi A (2011) On the minimax complexity of pricing in a changing environment. Oper. Res. 59(1):66–79.LinkGoogle Scholar
  • Blanchet JH, Glynn PW (2015) Unbiased Monte Carlo for optimization and functions of expectations via multi-level randomization. Proceedings of the Winter Simulation Conference (Institute of Electrical and Electronics Engineers, Washington, DC), 3656–3667.Google Scholar
  • Borkar VS (2008) Stochastic Approximation: A Dynamical Systems Viewpoint, vol. 48 (Hindustan Book Agency, Gurgaon, India).CrossrefGoogle Scholar
  • Cesa-Bianchi N, Lugosi G (2006) Prediction, Learning, and Games. (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Chick SE (2006) Bayesian ideas and discrete event simulation: why, what and how. Proceedings of the Winter Simulation Conference (Institute of Electrical and Electronics Engineers, Washington, DC), 96–105.Google Scholar
  • Chung KL (1954) On a stochastic approximation method. Ann. Math. Statist. 25(3):463–483.CrossrefGoogle Scholar
  • Duplay D, Lam H, Zhang X (2018) Achieving optimal bias-variance tradeoff in online derivative estimation. Proceedings of the Winter Simulation Conference, (Institute of Electrical and Electronics Engineers, Washington, DC).Google Scholar
  • Fabian V (1968) On asymptotic normality in stochastic approximation. Ann. Math. Statist. 39(4):1327–1332.CrossrefGoogle Scholar
  • Flaxman AD, Kalai AT, McMahan HB (2005) Online convex optimization in the bandit setting: gradient descent without a gradient. Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (Society for Industrial and Applied Mathematics), 385–394.Google Scholar
  • Fox BL, Glynn PW (1989) Replication schemes for limiting expectations. Probab. Engrg. Inform. Sci. 3(3):299–318.CrossrefGoogle Scholar
  • Fu MC (2006) Gradient estimation. Handb. Oper. Res. Manag. Sci. 13:575–616.Google Scholar
  • Fu MC, Hong LJ, Hu JQ (2009) Conditional Monte Carlo estimation of quantile sensitivities. Manage. Sci. 55(12):2019–2027.LinkGoogle Scholar
  • Fu MC, Hu JQ (1992) Extensions and generalizations of smoothed perturbation analysis in a generalized semi-Markov process framework. IEEE Trans. Automat. Control. 37(10):1483–1500.CrossrefGoogle Scholar
  • Giles MB (2008) Multilevel Monte Carlo path simulation. Oper. Res. 56(3):607–617.LinkGoogle Scholar
  • Glasserman P (2013) Monte Carlo Methods in Financial Engineering (Springer Science & Business Media, New York).Google Scholar
  • Glasserman P, Gong WB (1990) Smoothed perturbation analysis for a class of discrete-event systems. IEEE Trans. Automat. Control. 35(11):1218–1230.CrossrefGoogle Scholar
  • Glynn PW (1989) Optimization of stochastic systems via simulation. Proceedings of the Winter Simulation Conference (Institute of Electrical and Electronics Engineers, Washington, DC) 90–105.Google Scholar
  • Glynn PW (1990) Likelihood ratio gradient estimation for stochastic systems. Commun. ACM. 33(10):75–84.CrossrefGoogle Scholar
  • Glynn PW, Whitt W (1992) The asymptotic efficiency of simulation estimators. Oper. Res. 40(3):505–520.LinkGoogle Scholar
  • Gong WB, Ho YC (1987) Smoothed (conditional) perturbation analysis of discrete event dynamical systems. IEEE Trans. Automat. Control. 32(10):858–866.CrossrefGoogle Scholar
  • Hazan E (2016) Introduction to online convex optimization. Foundations and Trendsin Optimization 2(3-4):157–325.CrossrefGoogle Scholar
  • Heidelberger P, Cao XR, Zazanis MA, Suri R (1988) Convergence properties of infinitesimal perturbation analysis estimates. Management Sci. 34(11):1281–1302.LinkGoogle Scholar
  • Heidergott B, Vazquez-Abad FJ, Pflug G, Farenhorst-Yuan T (2010) Gradient estimation for discrete-event systems by measure-valued differentiation. ACM Trans. Model. Comput. Simul. 20(1):1–28.CrossrefGoogle Scholar
  • Heidergott B, Vázquez-Abad FJ (2008) Measure-valued differentiation for Markov Chains. J. Optim. Theory Appl. 136(2):187–209.CrossrefGoogle Scholar
  • Henderson SG (2003) Input model uncertainty: Why do we care and what should we do about it? Proceedings of the Winter Simulation Conference (Institute of Electrical and Electronics Engineers, Washington, DC), 90–100.Google Scholar
  • Ho YC, Cao X, Cassandras C (1983) Infinitesimal and finite perturbation analysis for queueing networks. Automatica J. IFAC. 19(4):439–445.CrossrefGoogle Scholar
  • Hong LJ (2009) Estimating quantile sensitivities. Oper. Res. 57(1):118–130.LinkGoogle Scholar
  • Kushner H, Yin GG (2003) Stochastic Approximation and Recursive Algorithms and Applications (Springer Science & Business Media, New York).Google Scholar
  • Lam H (2016) Advanced tutorial: Input uncertainty and robust analysis in stochastic simulation. Proceedings of the Winter Simulation Conference (IEEE), 178–192.Google Scholar
  • L’Ecuyer P (1990) A unified view of the IPA, SF, and LR gradient estimation techniques. Manage. Sci. 36(11):1364–1383.LinkGoogle Scholar
  • L’Ecuyer P (1991) An overview of derivative estimation. Proceedings of the Winter Simulation Conference (Institute of Electrical and Electronics Engineers, Washington, DC), 207–217.Google Scholar
  • McLeish D (2011) A general method for debiasing a Monte Carlo estimator. Monte Carlo Methods Appl. 17(4):301–315.CrossrefGoogle Scholar
  • Nemirovski A, Juditsky A, Lan G, Shapiro A (2009) Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4):1574–1609.CrossrefGoogle Scholar
  • Nesterov Y, Spokoiny V (2017) Random gradient-free minimization of convex functions. Found. Comput. Math. 17(2):527–566.CrossrefGoogle Scholar
  • Pasupathy R (2010) On choosing parameters in retrospective-approximation algorithms for stochastic root finding and simulation optimization. Oper. Res. 58(4-part-1):889–901.LinkGoogle Scholar
  • Pasupathy R, Kim S (2011) The stochastic root-finding problem: Overview, solutions, and open questions. ACM Trans. Model. Comput. Simul. 21(3):1–23.CrossrefGoogle Scholar
  • Peng Y, Fu MC, Hu JQ, Heidergott B (2018) A new unbiased stochastic derivative estimator for discontinuous sample performances with structural parameters. Oper. Res. 66(2):487–499.LinkGoogle Scholar
  • Polyak BT, Juditsky AB (1992) Acceleration of stochastic approximation by averaging. SIAM J. Control Optim. 30(4):838–855.CrossrefGoogle Scholar
  • Reiman MI, Weiss A (1989) Sensitivity analysis for simulations via likelihood ratios. Oper. Res. 37(5):830–844.LinkGoogle Scholar
  • Rhee Ch, Glynn PW (2015) Unbiased estimation with square root convergence for SDE models. Oper. Res. 63(5):1026–1043.LinkGoogle Scholar
  • Rubinstein RY (1986) The score function approach for sensitivity analysis of computer simulation models. Math. Comput. Simulation. 28(5):351–379.CrossrefGoogle Scholar
  • Rubinstein RY (1992) Sensitivity analysis of discrete event systems by the “push out” method. Ann. Oper. Res. 39(1):229–250.CrossrefGoogle Scholar
  • Ruppert D (1988) Efficient Estimations from a Slowly Convergent Robbins-Monro Process. Technical report. (Cornell University Operations Research and Industrial Engineering, Ithaca, NY).Google Scholar
  • Rychlik T (1990) Unbiased nonparametric estimation of the derivative of the mean. Statist. Probab. Lett. 10(4):329–333.CrossrefGoogle Scholar
  • Shalev-Shwartz S (2012) Online learning and online convex optimization. Foundations and Trends in Machine Learning 4(2):107–194.Google Scholar
  • Song E, Nelson BL, Pegden CD (2014) Advanced tutorial: Input uncertainty quantification. Proceedings of the Winter Simulation Conference, 162–176 (IEEE).Google Scholar
  • Spall JC (1992) Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Automat. Control. 37(3):332–341.CrossrefGoogle Scholar
  • Spall JC (1997) A one-measurement form of simultaneous perturbation stochastic approximation. Automatica J. IFAC. 33(1):109–112.CrossrefGoogle Scholar
  • Vihola M (2018) Unbiased estimators and multilevel Monte Carlo. Oper. Res. 66(2):448–462.LinkGoogle Scholar
  • Zazanis MA, Suri R (1993) Convergence rates of finite-difference sensitivity estimates for stochastic systems. Oper. Res. 41(4):694–703.LinkGoogle Scholar
  • Zhou K, Doyle JC (1998) Essentials of Robust Control (Prentice Hall, Upper Saddle River, NJ). Google Scholar
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