A Pareto Dominance Principle for Data-Driven Optimization

Published Online:https://doi.org/10.1287/opre.2021.0609

References

  • Aliprantis C, Border K (2007) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer, Berlin).Google Scholar
  • Ash R, Doléans-Dade CA (2000) Probability and Measure Theory (Academic Press, New York).Google Scholar
  • Ban G-Y, Rudin C (2019) The big data newsvendor: Practical insights from machine learning. Oper. Res. 67(1):90–108.LinkGoogle Scholar
  • Barndorff-Nielsen O (2014) Information and Exponential Families in Statistical Theory (John Wiley & Sons, Hoboken, NJ).CrossrefGoogle 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.LinkGoogle Scholar
  • Bennouna A, Van Parys BPG (2021) Learning and decision-making with data: Optimal formulations and phase transitions. Preprint, submitted September 14, https://arxiv.org/abs/ 2109.06911.Google Scholar
  • Berge C (1997) Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces, and Convexity (Courier Corporation, North Chelmsford, MA).Google Scholar
  • Bertsekas D (2009) Convex Optimization Theory (Athena Scientific, Nashua, NH).Google Scholar
  • Bertsimas D, Kallus N (2020) From predictive to prescriptive analytics. Management Sci. 66(3):1025–1044.LinkGoogle Scholar
  • Bertsimas D, Gupta V, Kallus N (2018) Robust sample average approximation. Math. Programming 171(1–2):217–282.CrossrefGoogle Scholar
  • Billingsley P (1961) Statistical methods in Markov chains. Ann. Math. Statist. 32:12–40.CrossrefGoogle Scholar
  • Blackwell D (1947) Conditional expectation and unbiased sequential estimation. Ann. Math. Statist. 18:105–110.CrossrefGoogle Scholar
  • Blanchet J, Kang Y, Murthy K (2019) Robust Wasserstein profile inference and applications to machine learning. J. Appl. Probabilities 56(3):830–857.CrossrefGoogle Scholar
  • Cover T, Thomas J (2006) Elements of Information Theory (Wiley, New York).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.LinkGoogle Scholar
  • Dembo A, Zeitouni O (2009) Large Deviations Techniques and Applications (Springer, Berlin).Google Scholar
  • Derman E, Mannor S (2020) Distributional robustness and regularization in reinforcement learning. Preprint, submitted March 5, https://arxiv.org/abs/ 2003.02894.Google Scholar
  • Dou X, Anitescu M (2019) Distributionally robust optimization with correlated data from vector autoregressive processes. Oper. Res. Lett. 47(4):294–299.CrossrefGoogle Scholar
  • Duchi J, Glynn P, Namkoong H (2021) Statistics of robust optimization: A generalized empirical likelihood approach. Math. Oper. Res. 46(3):946–969.LinkGoogle Scholar
  • Durrett R (2010) Probability: Theory and Examples (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Gao R (2023) Finite-sample guarantees for Wasserstein distributionally robust optimization: Breaking the curse of dimensionality. Oper. Res. 71(6):2291–2306.Google Scholar
  • Gupta V (2019) Near-optimal Bayesian ambiguity sets for distributionally robust optimization. Management Sci. 65(9):4242–4260.LinkGoogle Scholar
  • Hanasusanto G, Kuhn D, Wiesemann W (2016) A comment on “computational complexity of stochastic programming problems”. Math. Programming 159(1):557–569.CrossrefGoogle Scholar
  • Hu Y, Kallus N, Mao X (2022) Fast rates for contextual linear optimization. Management Sci. 68(6):4236–4245.LinkGoogle Scholar
  • Kantorovich LV, Rubinshtein GS (1958) On a space of totally additive functions. Vestnik Leningradskogo Universiteta 13(7):52–59.Google Scholar
  • King A, Tyrrell Rockafellar R (1993) Asymptotic theory for solutions in statistical estimation and stochastic programming. Math. Oper. Res. 18(1):148–162.LinkGoogle Scholar
  • King A, Wets RJ-B (1991) Epi-consistency of convex stochastic programs. Stochastic Stochastic Rep. 34(1–2):83–92.CrossrefGoogle Scholar
  • Koopman B (1936) On distributions admitting a sufficient statistic. Trans. Amer. Math. Soc. 39(3):399–409.CrossrefGoogle Scholar
  • Küchler U, Sørensen M (2006) Exponential Families of Stochastic Processes (Springer, Berlin).Google Scholar
  • Kuhn D, Esfahani PM, Nguyen VA, Shafieezadeh-Abadeh S (2019) Wasserstein distributionally robust optimization: Theory and applications in machine learning. Operations Research & Management Science in the Age of Analytics (INFORMS, Catonsville, MD), 130–166.LinkGoogle Scholar
  • Lam H (2019) Recovering best statistical guarantees via the empirical divergence-based distributionally robust optimization. Oper. Res. 67(4):1090–1105.AbstractGoogle Scholar
  • Le Maître O, Knio O (2010) Introduction: Uncertainty Quantification and Propagation (Springer, Berlin).Google Scholar
  • Lehmann EL, Casella G (1998) Theory of Point Estimation (Springer, Berlin).Google Scholar
  • Li M, Sutter T, Kuhn D (2021) Distributionally robust optimization with Markovian data. Meila M, Zhang T, eds. Proc. 38th Internat. Conf. Machine Learn., (PMLR, New York), 6493–6503.Google Scholar
  • Mohajerin Esfahani P, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Program. 171(1–2):115–166.CrossrefGoogle Scholar
  • Newey W, McFadden D (1994) Large sample estimation and hypothesis testing. Handbook of Econometrics (Elsevier, New York), 2111–2245.CrossrefGoogle Scholar
  • Rao R (1945) Information and the accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37:81–91.Google Scholar
  • Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Rockafellar RT, Roger J-B (1998) Wets Variational Analysis (Springer, Berlin).CrossrefGoogle Scholar
  • Ross S (2010) Introduction to Probability Models (Elsevier, New York).Google Scholar
  • Shapiro A (1989) Asymptotic properties of statistical estimators in stochastic programming. Ann. Statist. 17(2):841–858.CrossrefGoogle Scholar
  • Shapiro A (1990) On differential stability in stochastic programming. Math. Programming 47(1):107–116.CrossrefGoogle Scholar
  • Shapiro A (1991) Asymptotic analysis of stochastic programs. Ann. Oper. Res. 30(1–4):169–186.CrossrefGoogle Scholar
  • Shapiro A (1993) Asymptotic behavior of optimal solutions in stochastic programming. Math. Oper. Res. 18(4):829–845.LinkGoogle Scholar
  • Shapiro A (2003) Monte Carlo sampling methods. Stochastic Programming (Elsevier, New York), 353–425.CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Smith J, Winkler R (2006) The optimizer’s curse: Skepticism and postdecision surprise in decision analysis. Management Sci. 52(3):311–322.LinkGoogle Scholar
  • Sutter T, Krause A, Kuhn D (2021) Robust generalization despite distribution shift via minimum discriminating information. Ranzato M, Beygelzimer A, Dauphin Y, Liang PS, Wortman Vaughan J, eds. Advances in Neural Information Processing Systems, vol. 34 (Curran Associates, Inc., Red Hook, NY), 29754–29767.Google Scholar
  • Van Parys B (2021) Efficient data-driven optimization with noisy data. Preprint, submitted February 8, https://arxiv.org/abs/ 2102.04363.Google Scholar
  • Van Parys B, Esfahani PM, Kuhn D (2021) From data to decisions: Distributionally robust optimization is optimal. Management Sci. 67(6):3387–3402.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.