On Generalization and Regularization via Wasserstein Distributionally Robust Optimization

Published Online:https://doi.org/10.1287/mnsc.2023.03895

References

  • Abu-Mostafa YS, Magdon-Ismail M, Lin HT (2012) Learning from Data (AMLBook, New York).Google Scholar
  • Aolaritei L, Lanzetti N, Chen H, Dörfler F (2025) Distributional uncertainty propagation via optimal transport. IEEE Trans. Automatic Control 70(9):6080–6095.Google Scholar
  • Ban G-Y, Rudin C (2018) The big data newsvendor: Practical insights from machine learning. Oper. Res. 67(1):90–108.LinkGoogle Scholar
  • Bartl D, Drapeau S, Obloj J, Wiesel J (2020) Robust uncertainty sensitivity analysis. Preprint, submitted June 22, https://arxiv.org/abs/2006.12022.Google Scholar
  • Bawa VS (1975) Optimal rules for ordering uncertain prospects. J. Financial Econom. 2(1):95–91.CrossrefGoogle Scholar
  • Blanchet J, Kang Y (2021) Sample out-of-sample inference based on Wasserstein distance. Oper. Res. 69(3):985–1013.LinkGoogle Scholar
  • Blanchet J, Chen L, Zhou X (2022) Distributionally robust mean-variance portfolio selection with Wasserstein distances. Management Sci. 68(9):6382–6410.LinkGoogle Scholar
  • Blanchet J, Kang Y, Murthy K (2019) Robust Wasserstein profile inference and applications to machine learning. J. Appl. Probability 56(3):830–857.CrossrefGoogle Scholar
  • Blanchet J, Murthy K, Si N (2022) Confidence regions in Wasserstein distributionally robust estimation. Biometrika 109(2):295–315.CrossrefGoogle Scholar
  • Bobkov S, Ledoux M (2019) One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances, vol. 261 (American Mathematical Society, Providence, RI).CrossrefGoogle Scholar
  • Breiman L (1996) Bias, variance, and arcing classifiers. Technical report 460, Statistics Department, University of California, Berkeley.Google Scholar
  • Cai J, Li JYM, Mao T (2025) Distributionally robust optimization under distorted expectations. Oper. Res. 73(2):969–985.LinkGoogle Scholar
  • Chen R, Paschalidis IC (2018) A robust learning approach for regression models based on distributionally robust optimization. J. Machine Learn. Res. 19(1):1–48.Google Scholar
  • Chen L, He S, Zhang S (2011) Tight bounds for some risk measures, with applications to robust portfolio selection. Oper. Res. 59(4):847–865.LinkGoogle Scholar
  • Chew HC, Karni E, Safra Z (1987) Risk aversion in the theory of expected utility with rank dependent probabilities. J. Econom. Theory 42(2):370–381.CrossrefGoogle Scholar
  • Chu H, Lin M, Toh KC (2024) Wasserstein distributionally robust optimization and its tractable regularization formulations. Preprint, submitted February 6, https://arxiv.org/abs/2402.03942.Google Scholar
  • Drucker H, Burges CJC, Kaufman L, Smola A, Vapnik V (1997) Support vector regression machines. Adv. Neural Inform. Processing Systems 28(7):779–784.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):115–166.CrossrefGoogle Scholar
  • Fishburn PC (1977) Mean-risk analysis with risk associated with below target returns. Amer. Econom. Rev. 67(2):116–126.Google Scholar
  • Föllmer H, Shied A (2016) Stochastic Finance: An Introduction in Discrete Time, Fourth ed. (Walter de Gruyter, Berlin)Google Scholar
  • Fournier N, Guillin A (2015) On the rate of convergence in Wasserstein distance of the empirical measure. Probability Theory Related Fields 162(3):707–738.CrossrefGoogle Scholar
  • Gao R (2023) Finite-sample guarantees for Wasserstein distributionally robust optimization: Breaking the curse of dimensionality. Oper. Res. 71(6):2291–2306.LinkGoogle Scholar
  • Gao R, Chen X, Kleywegt AJ (2017) Wasserstein distributionally robust optimization and variation regularization. Preprint, submitted December 17, https://arxiv.org/abs/1712.06050.Google Scholar
  • Gao R, Chen X, Kleywegt AJ (2022) Wasserstein distributionally robust optimization and variation regularization. Oper. Res. 72(3):1177–1191.LinkGoogle Scholar
  • Gotoh J, Uryasev S (2017) Support vector machines based on convex risk functions and general norms. Ann. Oper. Res. 249:301–328.CrossrefGoogle Scholar
  • Krokhmal P (2007) Higher moment coherent risk measures. Quant. Finance 7(4):373–387.CrossrefGoogle 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 TutORials in Operations Research (INFORMS, Catonsville, MD), 130–166.Google Scholar
  • Lee YJ, Mangasarian OL (2001) SSVM: A smooth support vector machine for classification. Comput. Optim. Appl. 20:5–22.CrossrefGoogle Scholar
  • Lee YJ, Hsieh WF, Huang CM (2005) ε-SSVR: A smooth support vector machine for ε-insensitive regression. IEEE Trans. Knowledge Data Engrg. 17(5):678–685.CrossrefGoogle Scholar
  • Olea JLM, Rush C, Velez A, Wiesel J (2022) The out-of-sample prediction error of the square-root-LASSO and related estimators. Preprint, submitted November 14, https://arxiv.org/abs/2211.07608.Google Scholar
  • Quiggin J (1982) A theory of anticipated utility. J. Econom. Behav. Organ. 3(4):323–343.CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S (2013) The fundamental risk quadrangle in risk management, optimization and statistical estimation. Surveys Oper. Res. Management Sci. 18(1–2):33–53.CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S, Zabarankin M (2008) Risk tuning with generalized linear regression. Math. Oper. Res. 33(3):712–729.LinkGoogle Scholar
  • Schölkopf B, Bartlett P, Smola A, Williamson R (1998) Support vector regression with automatic accuracy control. Internat. Conf. Artificial Neural Networks (Springer London, London), 111–116.Google Scholar
  • Schölkopf B, Smola AJ, Williamson RC, Bartlett PL (2000) New support vector algorithms. Neural Comput. 12(5):1207–1245.CrossrefGoogle Scholar
  • Schmeidler D (1989) Subjective probability and expected utility without additivity. Econometrica 57(3):571–587.CrossrefGoogle Scholar
  • Shafieezadeh-Abadeh S, Kuhn D, Esfahani PM (2019) Regularization via mass transportation. J. Machine Learn. Res. 20(103):1–68.Google Scholar
  • Shafieezadeh-Abadeh S, Aolaritei L, Dörfler F, Kuhn D (2023) New perspectives on regularization and computation in optimal transport-based distributionally robust optimization. Preprint, submitted March 7, https://arxiv.org/abs/2303.03900.Google Scholar
  • Shalev-Shwartz S, Ben-David S (2014) Understanding Machine Learning: From Theory to Algorithms (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Sim M, Zhao L, Zhou M (2021) Tractable robust supervised learning models. Preprint, submitted December 14, https://doi.org/10.2139/ssrn.3981205.Google Scholar
  • Suykens J, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Processing Lett. 9:293–300.CrossrefGoogle Scholar
  • Volpi R, Namkoong H, Sener O, Duchi JC, Murino V, Savarese S (2018) Generalizing to unseen domains via adversarial data augmentation. Adv. Neural Inform. Processing Systems 31:5334–5344.Google Scholar
  • Wang R, Wei Y, Willmot GE (2020) Characterization, robustness and aggregation of signed Choquet integrals. Math. Oper. Res. 45(3):993–1015.LinkGoogle Scholar
  • Wozabal D (2014) Robustifying convex risk measures for linear portfolios: A nonparametric approach. Oper. Res. 62(6):1302–1315.LinkGoogle Scholar
  • Yaari ME (1987) The dual theory of choice under risk. Econometrica 55(1):95–115.CrossrefGoogle Scholar
  • Zhang L, Yang J, Gao R (2024) Optimal robust policy for feature-based newsvendor. Management Sci. 70(4):2315–2329.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.