A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization

Published Online:https://doi.org/10.1287/opre.2023.0135

References

  • Aliprantis CD, Border K (2006) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer Science & Business Media, Boston).Google Scholar
  • Ambrosio L, Fusco N, Pallara D (2000) Functions of Bounded Variation and Free Discontinuity Problems (Oxford University Press, Oxford, UK).CrossrefGoogle Scholar
  • Aubin JP, Frankowska H (2009) Set-Valued Analysis (Springer Science & Business Media, Boston).CrossrefGoogle Scholar
  • Bertsekas DP, Shreve SE (1996) Stochastic Optimal Control: The Discrete-Time Case, vol. 5 (Athena Scientific, Belmont, MA).Google Scholar
  • Blanchet J, Murthy K (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.LinkGoogle Scholar
  • Blanchet J, Murthy K, Nguyen VA (2021) Statistical analysis of Wasserstein distributionally robust estimators. Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications (INFORMS), 227–254.LinkGoogle Scholar
  • Castaing C, Valadier M (1977) Measurable multifunctions. Convex Analysis and Measurable Multifunctions (Springer, Berlin), 59–90.CrossrefGoogle Scholar
  • Chen Z, Kuhn D, Wiesemann W (2023) On approximations of data-driven chance constrained programs over Wasserstein balls. Oper. Res. Lett. 51(3):226–233.CrossrefGoogle Scholar
  • Föllmer H, Schied A (2010) Convex and coherent riskmeasures. Encyclopedia of Quantitative Finance, 355–363.Google Scholar
  • Gao R, Kleywegt A (2023) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res. 48(2):603–655.LinkGoogle Scholar
  • Kallenberg O (1997) Foundations of Modern Probability, vol. 2 (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
  • Liu F, Chen Z, Wang S (2023) Globalized distributionally robust counterpart. INFORMS J. Comput. 35(5):1120–1142.LinkGoogle Scholar
  • Luenberger DG (1997) Optimization by Vector Space Methods (John Wiley & Sons, New York).Google 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
  • Rockafellar RT (1970) Convex Analysis, Number 28 in Princeton Mathematical Series (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Rockafellar RT, Uryasev S (2000) Optimization of conditional value at-risk. J. Risk 2:21–42.Google Scholar
  • Rockafellar RT, Wets RJB (2009) Variational Analysis, vol. 317 (Springer Science & Business Media, Boston).Google Scholar
  • Shapiro A (2001) On duality theory of conic linear problems. Semi-Infinite Programming (Springer, Berlin), 135–165.CrossrefGoogle Scholar
  • Shapiro A (2017) Interchangeability principle and dynamic equations in risk averse stochastic programming. Oper. Res. Lett. 45(4):377–381.CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczynski A (2021) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Shreve SE, Bertsekas DP (1979) Universally measurable policies in dynamic programming. Math. Oper. Res. 4(1):15–30.LinkGoogle Scholar
  • Sinha A, Namkoong H, Duchi J (2018) Certifying some distributional robustness with principled adversarial training. Proc. Internat. Conf. Learn. Representations (ICLR, Appleton, WI).Google Scholar
  • Wang J, Gao R, Zha H (2022) Reliable off-policy evaluation for reinforcement learning. Oper. Res. 72(2):699–716.Google Scholar
  • Xie W (2021) On distributionally robust chance constrained programs with Wasserstein distance. Math. Programming 186(1):115–155.CrossrefGoogle Scholar
  • Yang I (2017) A convex optimization approach to distributionally robust Markov decision processes with Wasserstein distance. IEEE Control Systems Lett. 1(1):164–169.CrossrefGoogle Scholar
  • Yang Z, Gao R (2022) Wasserstein Regularization for 0-1 Loss (Optimization Online).Google Scholar
  • Zhao C, Guan Y (2018) Data-driven risk-averse stochastic optimization with Wasserstein metric. Oper. Res. Lett. 46(2):262–267.CrossrefGoogle Scholar
  • Zhen J, Kuhn D, Wiesemann W (2023) A unified theory of robust and distributionally robust optimization via the primal-worst-equals-dual-best principle. Oper. Res., ePub ahead of print September 26, https://doi.org/10.1287/opre.2021.0268.Google 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.