From Data to Decisions: Distributionally Robust Optimization Is Optimal

Published Online:https://doi.org/10.1287/mnsc.2020.3678

References

  • Ahmadi-Javid A (2012) Entropic value-at-risk: A new coherent risk measure. J. Optim. Theory Appl. 155(3):1105–1123.CrossrefGoogle Scholar
  • Baire R (1899) Sur les fonctions de variables réelles. Ann. Mat. Pura Appl. 3(3):1–123.CrossrefGoogle Scholar
  • Bayraksan G , Love DK (2015) Data-driven stochastic programming using phi-divergences. Aleman DM, Thiele AC, eds. The Operations Research Revolution (INFORMS, Catonsville, MD), 1–19.LinkGoogle 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
  • Berge C (1963) Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces, and Convexity (Oliver & Boyd, London).Google Scholar
  • Bertsimas D , Gupta V , Kallus N (2018a) Robust sample average approximation. Math. Program. 171(1):217–282.CrossrefGoogle Scholar
  • Bertsimas D , Gupta V , Kallus N (2018b) Data-driven robust optimization. Math. Programming 167(2):235–292.CrossrefGoogle Scholar
  • Bledsoe W (1952) Neighborly functions. Hedlund GA, Hochschild GP, Schaeffer AC, eds. Proceedings of the American Mathematical Society, vol. 3 (American Mathematical Society, Menasha, WI), 114–115.Google Scholar
  • Calafiore GC (2007) Ambiguous risk measures and optimal robust portfolios. SIAM J. Optim. 18(3):853–877.CrossrefGoogle Scholar
  • Cover TM , Thomas JA (2006) Elements of Information Theory (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • Csiszár I (2006) A simple proof of Sanov’s theorem. Bull. Brazilian Math. Soc. 37(4):453–459.CrossrefGoogle 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
  • Duchi J , Glynn P , Namkoong H (2016) Statistics of robust optimization: A generalized empirical likelihood approach. Preprint, submitted October 11, https://arxiv.org/abs/1610.03425.Google Scholar
  • Dupačová J , Wets R (1988) Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. Ann. Statist. 16(4):1517–1549.CrossrefGoogle Scholar
  • Erdoğan E , Iyengar G (2006) Ambiguous chance constrained problems and robust optimization. Math. Programming 107(1–2):37–61.CrossrefGoogle Scholar
  • Gupta V (2019) Near-optimal Bayesian ambiguity sets for distributionally robust optimization. Management Sci. 65(9):4242–4260.Google Scholar
  • Hu Z , Hong LJ (2013) Kullback-Leibler divergence constrained distributionally robust optimization. Accessed November 11, 2020, http://www.optimization-online.org/DB_FILE/2012/11/3677.pdf. Google Scholar
  • Jiang R , Guan Y (2018) Risk-averse two-stage stochastic program with distributional ambiguity. Oper. Res. 66(5):1390–1405.LinkGoogle Scholar
  • Kullback S , Leibler RA (1951) On information and sufficiency. Ann. Math. Statist. 22(1):79–86.CrossrefGoogle Scholar
  • Lam H (2016) Robust sensitivity analysis for stochastic systems. Math. Oper. Res. 41(4):1248–1275.LinkGoogle Scholar
  • Lam H (2019) Recovering best statistical guarantees via the empirical divergence-based distributionally robust optimization. Oper. Res. 67(4):1090–1105.Google Scholar
  • Le Maître OP , Knio OM (2010) Introduction: Uncertainty quantification and propagation. Le Maitre OP, Knio OM, eds. Spectral Methods for Uncertainty Quantification (Springer, Dordrecht, Netherlands).Google Scholar
  • Matejdes M (1987) Sur les sélecteurs des multifonctions. Math. Slovaca 37(1):111–124.Google Scholar
  • Michaud RO (1989) The Markowitz optimization enigma: Is ‘optimized’ optimal? Financial Analysts J. 45(1):31–42.CrossrefGoogle Scholar
  • Mohajerin Esfahani P , Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1–2):115–166.CrossrefGoogle Scholar
  • Nesterov Y , Nemirovskii A (1994) Interior-Point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Nikodym O (1930) Sur une généralisation des intégrales de M.J. Radon. Fundamenta Math. 15(1):131–179.CrossrefGoogle Scholar
  • Owen AB (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75(2):237–249.CrossrefGoogle Scholar
  • Parpas P , Ustun B , Webster M , Tran Q (2015) Importance sampling in stochastic programming: A Markov chain Monte Carlo approach. INFORMS J. Comput. 27(2):358–377.LinkGoogle Scholar
  • Pflug G , Wozabal D (2007) Ambiguity in portfolio selection. Quant. Finance 7(4):435–442.CrossrefGoogle Scholar
  • Prokhorov YV (1956) Convergence of random processes and limit theorems in probability theory. Theory Probab. Appl. 1(2):157–214.CrossrefGoogle Scholar
  • Rockafellar RT , Wets RJ-B (1998) Variational Analysis (Springer, Dordrecht, Netherlands).CrossrefGoogle Scholar
  • Shapiro A , Dentcheva D , Ruszczyńsk A (2014) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Smith JE , Winkler RL (2006) The optimizer’s curse: Skepticism and postdecision surprise in decision analysis. Management Sci. 52(3):311–322.LinkGoogle Scholar
  • Sun H , Xu H (2016) Convergence analysis for distributionally robust optimization and equilibrium problems. Math. Oper. Res. 41(2):377–401.LinkGoogle Scholar
  • Van Erven T , Harremoës P (2014) Rényi divergence and Kullback-Leibler divergence. IEEE Trans. Inform. Theory 60(7):3797–3820.CrossrefGoogle Scholar
  • Wang Z , Glynn PW , Ye Y (2016) Likelihood robust optimization for data-driven newsvendor problems. Comput. Management Sci. 12(2):241–261.CrossrefGoogle Scholar
  • Zeitouni O , Ziv J , Merhav N (1992) When is the generalized likelihood ratio test optimal? IEEE Trans. Inform. Theory 38(5):1597–1602.CrossrefGoogle Scholar
  • Zhao C , Guan Y (2018) Data-driven risk-averse stochastic optimization with Wasserstein metric. Oper. Res. Lett. 46(2):262–267.CrossrefGoogle 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.