Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization

References

• Adler RJ (1990) An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, Lecture Notes—Monograph Series (Institute of Mathematical Statistics, Hayward, CA).Google Scholar
• Adler RJ, Taylor JE (2007) Random Fields and Geometry (Springer Science & Business Media, New York).Google Scholar
• Adler R, Taylor JE (2011) Topological Complexity of Smooth Random Functions (Springer-Verlag, Berlin, Heidelberg).Crossref, Google Scholar
• Adler RJ, Blanchet JH, Liu J (2012) Efficient Monte Carlo for high excursions of Gaussian random fields. Ann. Appl. Probab. 22(3):1167–1214.Crossref, Google Scholar
• Adler RJ, Taylor JE, Worsley KJ (2009) Applications of random fields and geometry: Foundations and case studies. Accessed May 30, 2016, http://webee.technion.ac.il/people/adler/hrf.pdf.Google Scholar
• Agresti A (2013) Categorical Data Analysis, 3rd ed., Wiley Series in Probability and Statistics (John Wiley & Sons, Inc., Hoboken, NJ).Google Scholar
• Atlason J, Epelman MA, Henderson SG (2004) Call center staffing with simulation and cutting plane methods. Ann. Oper. Res. 127(1–4):333–358.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
• Bertsimas D, Gupta V, Kallus N (2018) Robust sample average approximation. Math. Programming 171(1/2):217–282.Google Scholar
• Blanchet J, Kang Y (2016) Sample out-of-sample inference based on Wasserstein distance. Working paper, Columbia University, New York.Google Scholar
• Blanchet J, Murthy K (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.Link, Google Scholar
• Blanchet J, Kang Y, Murthy K (2016) Robust Wasserstein profile inference and applications to machine learning. Working paper, Columbia University, New York.Google Scholar
• Chen J, Huang Y (2013) Finite-sample properties of the adjusted empirical likelihood. J. Nonparametric Statist. 25(1):147–159.Crossref, Google Scholar
• Cox DR, Hinkley DV (1974) Theoretical Statistics (CRC Press, Boca Raton, FL).Crossref, 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
• DiCiccio T, Hall P, Romano J (1991) Empirical likelihood is Bartlett-correctable. Ann. Statist. 19(2):1053–1061.Crossref, Google Scholar
• Duchi J, Glynn P, Namkoong H (2019) Statistics of robust optimization: A generalized empirical likelihood approach. Math. Oper. Res. Forthcoming.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
• Fábián CI (2008) Handling CVaR objectives and constraints in two-stage stochastic models. Eur. J. Oper. Res. 191(3):888–911.Crossref, Google Scholar
• Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: An overview. Eur. J. Oper. Res. 235(3):471–483.Crossref, Google Scholar
• Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with Wasserstein distance. Working paper, Georgia Institute of Technology, Atlanta.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
• Gotoh JY, Kim MJ, Lim AE (2018) Robust empirical optimization is almost the same as mean-variance optimization. Oper. Res. Lett. 46(4):448–452.Crossref, Google Scholar
• Gupta V (2019) Near-optimal ambiguity sets for distributionally robust optimization. Management Sci., ePub ahead of print March 18, https://doi.org/10.1287/mnsc.2018.3140.Link, Google Scholar
• Hu Z, Hong LJ (2013) Kullback-Leibler divergence constrained distributionally robust optimization. Optim. Online. Available at http://www.optimization-online.org/DB_FILE/2012/11/3677.pdf.Google Scholar
• Jiang R, Guan Y (2016) Data-driven chance constrained stochastic program. Math. Programming 158(1/2):291–327.Crossref, Google Scholar
• Krokhmal P, Palmquist J, Uryasev S (2002) Portfolio optimization with conditional value-at-risk objective and constraints. J. Risk 4(2):43–68.Crossref, Google Scholar
• Kullback S, Leibler RA (1951) On information and sufficiency. Ann. Math. Statist. 22(1):79–86.Crossref, Google Scholar
• Lam H (2016) 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, Qian H (2016) The empirical likelihood approach to simulation input uncertainty. Proc. 2016 Winter Simulation Conf. (IEEE, Piscataway, NJ), 791–802.Crossref, Google Scholar
• Lam H, Zhou E (2015) Quantifying uncertainty in sample average approximation. Proc. 2015 Winter Simulation Conf. (IEEE, Piscataway, NJ), 3846–3857.Crossref, Google Scholar
• Lam H, Zhou E (2017) The empirical likelihood approach to quantifying uncertainty in sample average approximation. Oper. Res. Lett. 45(4):301–307.Crossref, Google Scholar
• Lang A, Potthoff J (2011) Fast simulation of Gaussian random fields. Monte Carlo Methods Appl. 17(3):195–214.Crossref, Google Scholar
• Liu Y, Chen J (2010) Adjusted empirical likelihood with high-order precision. Ann. Statist. 38(3):1341–1362.Crossref, Google Scholar
• Love D, Bayraksan G (2015) Phi-divergence constrained ambiguous stochastic programs for data-driven optimization. Technical report, The Ohio State University, Columbus.Google Scholar
• Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2):674–699.Crossref, Google Scholar
• Maurer A, Pontil M (2009) Empirical Bernstein bounds and sample variance penalization. arXiv:0907.3740.Google Scholar
• Moon K, Hero A (2014) Multivariate f-divergence estimation with confidence. Proc. Adv. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 2420–2428.Google Scholar
• Nagaraj K, Pasupathy R (2014) Stochastically constrained simulation optimization on integer-ordered spaces: The cgR-SPLINE algorithm. Technical report, Purdue University, West Lafayette, IN.Google Scholar
• Namkoong H, Duchi JC (2017) Variance-based regularization with convex objectives. Proc. Adv. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 2975–2984.Google Scholar
• Nguyen X, Wainwright MJ, Jordan MI (2008) Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization. Proc. Adv. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 1089–1096.Google Scholar
• Owen AB (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75(2):237–249.Crossref, Google Scholar
• Owen AB (2001) Empirical Likelihood (CRC Press, New York).Crossref, Google Scholar
• Pál D, Póczos B, Szepesvári C (2010) Estimation of Rényi entropy and mutual information based on generalized nearest-neighbor graphs. Proc. Adv. Neural Inform. Processing Systems (Curran Associates, Red Hook, NY), 1849–1857.Google Scholar
• Pardo L (2005) Statistical Inference Based on Divergence Measures (CRC Press, New York).Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory, vol. 16 (SIAM, Philadelphia).Crossref, Google Scholar
• Tsao M (2004a) Bounds on coverage probabilities of the empirical likelihood ratio confidence regions. Ann. Statist. 32(3):1215–1221.Crossref, Google Scholar
• Tsao M (2004b) A new method of calibration for the empirical loglikelihood ratio. Statist. Probab. Lett. 68(3):305–314.Crossref, Google Scholar
• Tsao M, Wu F (2013) Empirical likelihood on the full parameter space. Ann. Statist. 41(4):2176–2196.Crossref, Google Scholar
• van der Vaart AW, Wellner JA (1996) Weak Convergence and Empirical Processes: With Applications in Statistics (Springer, New York).Crossref, Google Scholar
• Wang W, Ahmed S (2008) Sample average approximation of expected value constrained stochastic programs. Oper. Res. Lett. 36(5):515–519.Crossref, Google Scholar
• Wang Z, Glynn PW, Ye Y (2015) Likelihood robust optimization for data-driven problems. Comput. Management Sci. 13(2):241–261.Crossref, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Wood AT, Chan G (1994) Simulation of stationary Gaussian processes in [0,1]d. J. Comput. Graphical Statist. 3(4):409–432.Google Scholar