Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees

References

• Bandi C, Bertsimas D (2012) Tractable stochastic analysis in high dimensions via robust optimization. Math. Programming 134(1):23–70.Crossref, Google Scholar
• Banks J, Carson JS, Nelson BL, Nicol DM (2009) Discrete-Event System Simulation, 5th ed. (Prentice Hall, Englewood Cliffs, NJ).Google Scholar
• Barton RR, Nelson BL, Xie W (2013) Quantifying input uncertainty via simulation confidence intervals. INFORMS J. Comput. 26(1):74–87.Link, Google Scholar
• Barton RR, Schruben LW (1993) Uniform and bootstrap resampling of empirical distributions. Evans GW, Mollaghasemi M, Russell EC, Biles WE, eds. Proc. 1993 Winter Simulation Conf. (ACM, New York), 503–508.Crossref, Google Scholar
• Barton RR, Schruben LW (2001) Resampling methods for input modeling. Peters BA, Smith JS, Medeiros DJ, Rohrer MW, eds. Proc. 2001 Winter Simulation Conf., vol. 1 (IEEE, New York), 372–378.Crossref, Google Scholar
• Bayraksan G, Love DK (2015) Data-driven stochastic programming using phi-divergences. Aleman DM, Thiele AC, eds. The Operations Research Revolution, INFORMS TutORials in Operations Research (INFORMS, Cantonsville, MD), 1–9.Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Bertsekas DP (1999) Nonlinear Programming (Athena Scientific, Nashua, NH).Google Scholar
• Bertsimas D, Natarajan K (2007) A semidefinite optimization approach to the steady-state analysis of queueing systems. Queueing Systems 56(1):27–39.Crossref, Google Scholar
• Bertsimas D, Popescu I (2005) Optimal inequalities in probability theory: A convex optimization approach. SIAM J. Optim. 15(3):780–804.Crossref, Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
• Bertsimas D, Gupta V, Kallus N (2018) Robust sample average approximation. Math. Programming 171(1/2):217–282.Crossref, Google Scholar
• Birge JR, Wets RJ-B (1987) Computing bounds for stochastic programming problems by means of a generalized moment problem. Math. Oper. Res. 12(1):149–162.Link, Google Scholar
• Blanchet J, Murthy KRA (2016) Quantifying distributional model risk via optimal transport. arXiv preprint arXiv:1604.01446.Google Scholar
• Blanchet J, Kang Y, Murthy K (2016) Robust Wasserstein profile inference and applications to machine learning. arXiv preprint arXiv:1610.05627.Google Scholar
• Buche R, Kushner HJ (2002) Rate of convergence for constrained stochastic approximation algorithms. SIAM J. Control Optim. 40(4):1011–1041.Crossref, Google Scholar
• Canon MD, Cullum CD (1968) A tight upper bound on the rate of convergence of Frank-Wolfe algorithm. SIAM J. Control 6(4):509–516.Crossref, Google Scholar
• Cario M, Nelson BL (1997) Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical report, Citeseer. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.48.281&rep=rep1&type=pdf.Google Scholar
• Channouf N, L’Ecuyer P (2009) Fitting a normal copula for a multivariate distribution with both discrete and continuous marginals. Rossetti MD, Hill RR, Johansson B, Dunkin A, Ingalls RG, eds. Proc. Winter Simulation Conf. (IEEE, New York), 352–358.Crossref, Google Scholar
• Cheng RCH, Holland W (1997) Sensitivity of computer simulation experiments to errors in input data. J. Statist. Comput. Simulation 57(1–4):219–241.Crossref, Google Scholar
• Cheng RCH, Holland W (1998) Two-point methods for assessing variability in simulation output. J. Statist. Comput. Simulation 60(3):183–205.Crossref, Google Scholar
• Cheng RCH, Holland W (2004) Calculation of confidence intervals for simulation output. ACM Trans. Model. Comput. Simulation 14(4):344–362.Crossref, Google Scholar
• Chick SE (2001) Input distribution selection for simulation experiments: Accounting for input uncertainty. Oper. Res. 49(5):744–758.Link, Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• Duchi JC, Glynn PW, Namkoong H (2016) Statistics of robust optimization: A generalized empirical likelihood approach. arXiv preprint arXiv:1610.03425.Google Scholar
• Dunn JC (1979) Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals. SIAM J. Control Optim. 17(2):187–211.Crossref, Google Scholar
• Dunn JC (1980) Convergence rates for conditional gradient sequences generated by implicit step length rules. SIAM J. Control Optim. 18(5):473–487.Crossref, Google Scholar
• Dupuis P, Katsoulakis MA, Pantazis Y, Plechác P (2016) Path-space information bounds for uncertainty quantification and sensitivity analysis of stochastic dynamics. SIAM/ASA J. Uncertainty Quant. 4(1):80–111.Crossref, Google Scholar
• Esfahani PM, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1/2):115–166.Crossref, Google Scholar
• Fan W, Jeff Hong L, Zhang X (2013) Robust selection of the best. Pasupathy R, Kim S-H, Tolk A, Hill R, Kuhl ME, eds. Proc. 2013 Winter Simulation Conf. (IEEE Press, New York), 868–876.Crossref, Google Scholar
• Frank M, Wolfe P (1956) An algorithm for quadratic programming. Naval Res. Logist. Quart. 3(1–2):95–110.Crossref, Google Scholar
• Freund RM, Grigas P (2016) New analysis and results for the Frank–Wolfe method. Math. Programming 155(1-2):199–230.Google Scholar
• Fu MC (1994) Optimization via simulation: A review. Ann. Oper. Res. 53(1):199–247.Crossref, Google Scholar
• Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with Wasserstein distance. arXiv preprint arXiv:1604.02199.Google Scholar
• Ghosh S, Henderson SG (2002) Chessboard distributions and random vectors with specified marginals and covariance matrix. Oper. Res. 50(5):820–834.Link, Google Scholar
• Glasserman P, Xu X (2013) Robust portfolio control with stochastic factor dynamics. Oper. Res. 61(4):874–893.Link, Google Scholar
• Glasserman P, Xu X (2014) Robust risk measurement and model risk. Quant. Finance 14(1):29–58.Crossref, Google Scholar
• Glasserman P, Yang L (2018) Bounding wrong-way risk in CVA calculation. Math. Finance 28(1):268–305.Crossref, Google Scholar
• Glynn PW (1990) Likelihood ratio gradient estimation for stochastic systems. Comm. ACM 33(10):75–84.Crossref, Google Scholar
• Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4-Part-1):902–917.Link, Google Scholar
• Hampel FR (1974) The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69(346):383–393.Crossref, Google Scholar
• Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (2011) Robust Statistics: The Approach Based on Influence Functions, Wiley Series in Probability and Statistics (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Hansen LP, Sargent TJ (2001) Robust control and model uncertainty. Amer. Econom. Rev. 1(2):60–66.Crossref, Google Scholar
• Hansen LP, Sargent TJ (2008) Robustness (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Hazan E, Luo H (2016) Variance-reduced and projection-free stochastic optimization. arXiv preprint arXiv:1602.02101.Google Scholar
• Hu Z, Cao J, Jeff Hong L (2012) Robust simulation of global warming policies using the DICE model. Management Sci. 58(12):2190–2206.Link, Google Scholar
• Iyengar GN (2005) Robust dynamic programming. Math. Oper. Res. 30(2):257–280.Link, Google Scholar
• Jaggi M (2013) Revisiting Frank-Wolfe: Projection-free sparse convex optimization. Dasgupta S, McAllester D, eds. Proc. 30th Internat. Conf. Machine Learn. (ICML-13) (ACM, New York), 427–435.Google Scholar
• Jain A, Lim A, Shanthikumar J (2010) On the optimality of threshold control in queues with model uncertainty. Queueing Systems 65(2):157–174.Crossref, Google Scholar
• Kleinrock L (1976) Queueing Systems, vol. 2, Computer Applications (Wiley-Interscience, Hoboken, NJ).Google Scholar
• Kushner H, Yin G (2003) Stochastic Approximation and Recursive Algorithms and Applications, 2nd ed. (Springer-Verlag, New York).Google Scholar
• Kushner HJ (1974) Stochastic approximation algorithms for constrained optimization problems. Ann. Statist. 2(4):713–723.Crossref, Google Scholar
• Lafond J, Wai H-T, Moulines E (2016) On the online Frank-Wolfe algorithms for convex and non-convex optimizations. arXiv preprint arXiv:1510.01171.Google Scholar
• Lam H (2016a) Recovering best statistical guarantees via the empirical divergence-based distributionally robust optimization. arXiv preprint arXiv:1605.09349.Google Scholar
• Lam H (2016b) Robust sensitivity analysis for stochastic systems. Math. Oper. Res. 41(4):1248–1275.Link, Google Scholar
• Lam H (2018) Sensitivity to serial dependency of input processes: A robust approach. Management Sci. 64(3):1311–1327.Link, Google Scholar
• Lam H, Zhou E (2015) Quantifying uncertainty in sample average approximation. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (IEEE Press, New York), 3846–3857.Crossref, Google Scholar
• Lim AEB, Shanthikumar JG (2007) Relative entropy, exponential utility, and robust dynamic pricing. Oper. Res. 55(2):198–214.Link, Google Scholar
• Lim AEB, Shanthikumar JG, Shen ZJM (2006) Model uncertainty, robust optimization and learning. Johnson MP, Norman B, Secomandi N, eds. Models, Methods, and Applications for Innovative Decision Making, INFORMS TutORials in Operations Research (INFORMS, Cantonsville, MD), 66–94.Google Scholar
• Lim AEB, Shanthikumar JG, Watewai T (2011) Robust asset allocation with benchmarked objectives. Math. Finance 21(4):643–679.Google Scholar
• Lurie PM, Goldberg MS (1998) An approximate method for sampling correlated random variables from partially-specified distributions. Management Sci. 44(2):203–218.Link, Google Scholar
• Nemirovski A, Juditsky A, Lan G, Shapiro A (2009) Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4):1574–1609.Crossref, Google Scholar
• Nilim A, El Ghaoui L (2005) Robust control of Markov decision processes with uncertain transition matrices. Oper. Res. 53(5):780–798.Link, Google Scholar
• Owen AB (2001) Empirical Likelihood (CRC Press, Boca Raton, FL).Crossref, Google Scholar
• Pardo L (2005) Statistical Inference Based on Divergence Measures (CRC Press, Boca Raton, FL).Crossref, Google Scholar
• Pasupathy R, Kim S (2011) The stochastic root-finding problem: Overview, solutions, and open questions. ACM Trans. Model. Comput. Simulation 21(3):1–23.Crossref, Google Scholar
• Petersen IR, James MR, Dupuis P (2000) Minimax optimal control of stochastic uncertain systems with relative entropy constraints. IEEE Trans. Automatic Control 45(3):398–412.Crossref, Google Scholar
• Qian P, Wang Z, Wen Z (2015) A composite risk measure framework for decision making under uncertainty. arXiv preprint arXiv:1501.01126.Google Scholar
• Reddi SJ, Sra S, Poczos B, Smola A (2016) Stochastic Frank-Wolfe methods for nonconvex optimization. arXiv preprint arXiv:1607.08254.Google Scholar
• Reiman MI, Weiss A (1989) Sensitivity analysis for simulations via likelihood ratios. Oper. Res. 37(5):830–844.Link, Google Scholar
• Rubinstein RY (1986) The score function approach for sensitivity analysis of computer simulation models. Math. Comput. Simulation 28(5):351–379.Crossref, Google Scholar
• Ryzhov IO, Defourny B, Powell WB (2012) Ranking and selection meets robust optimization. Laroque C, Himmelspach J, Pasupathy R, Rose O, Uhrmacher AM, eds. Proc. 2012 Winter Simulation Conf. (IEEE, New York), 477–487.Crossref, Google Scholar
• Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput. Phys. Comm. 181(2):259–270.Crossref, Google Scholar
• Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global Sensitivity Analysis: The Primer (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Serfling RJ (2009) Approximation Theorems of Mathematical Statistics, Wiley Series in Probability and Statistics (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Shafieezadeh-Abadeh S, Esfahani PM, Kuhn D (2015) Distributionally robust logistic regression. Cortes C, Lee DD, Sugiyama M, Garnett R, eds. Proc. 28th Internat. Conf. Neural Inform. Processing Systems, vol. 1 (MIT Press, Cambridge, MA), 1576–1584.Google Scholar
• Smith JE (1993) Moment methods for decision analysis. Management Sci. 39(3):340–358.Link, Google Scholar
• Smith JE (1995) Generalized Chebyshev inequalities: Theory and applications in decision analysis. Oper. Res. 43(5):807–825.Link, Google Scholar
• Song E, Nelson BL (2015) Quickly assessing contributions to input uncertainty. IIE Trans. 47(9):893–909.Crossref, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Xie W, Nelson BL, Barton RR (2014) A Bayesian framework for quantifying uncertainty in stochastic simulation. Oper. Res. 62(6):1439–1452.Link, Google Scholar
• Xie W, Nelson BL, Barton RR (2015) Statistical uncertainty analysis for stochastic simulation. Working paper, Rensselaer Polytechnic Institute, Troy, NY. https://pdfs.semanticscholar.org/3ab3/ba63393f18e6a7c5af858e869edbd729d556.pdf.Google Scholar
• Xin L, Goldberg DA (2015) Distributionally robust inventory control when demand is a martingale. arXiv preprint arXiv:1511.09437.Google Scholar
• Xu H, Mannor S (2012) Distributionally robust Markov decision processes. Math. Oper. Res. 37(2):288–300.Link, Google Scholar
• Zhou E, Xie W (2015) Simulation optimization when facing input uncertainty. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (IEEE Press, New York), 3714–3724.Crossref, Google Scholar
• Zouaoui F, Wilson JR (2003) Accounting for parameter uncertainty in simulation input modeling. IIE Trans. 35(9):781–792.Crossref, Google Scholar
• Zouaoui F, Wilson JR (2004) Accounting for input-model and input-parameter uncertainties in simulation. IIE Trans. 36(11):1135–1151.Crossref, Google Scholar