R. Gao, X. Chen, and A. J. Kleywegt. Wasserstein distributionally robust optimization and variation regularization. Operations Research, 2022.
C. A. García Trillos and N. García Trillos. On the regularized risk of distributionally robust learning over deep neural networks. *Res Math Sci*, 9(3):54, Aug. 2022.
I. Gilboa and D. Schmeidler. Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18(2):141-153, 1989.
I. Goodfellow, J. Shlens, and C. Szegedy. Explaining and harnessing adversarial examples. In International Conference on Learning Representations, 2015.
S. Gowal, C. Qin, J. Uesato, T. Mann, and P. Kohli. Uncovering the limits of adversarial training against norm-bounded adversarial examples. arXiv preprint arXiv:2010.03593, 2020.
S. Gowal, S.-A. Rebuffi, O. Wiles, F. Stimberg, D. A. Calian, and T. A. Mann. Improving robustness using generated data. In Advances in Neural Information Processing Systems, volume 34, pages 4218-4233. Curran Associates, Inc., 2021.
G. Guo and J. Obloj. Computational methods for martingale optimal transport problems. The Annals of Applied Probability, 29(6):3311 - 3347, 2019.
L. P. Hansen and M. Marinacci. Ambiguity aversion and model misspecification: an economic perspective. Statistical Science, 31(4):511-515, 2016.
M. Hein and M. Andriushchenko. Formal guarantees on the robustness of a classifier against adversarial manipulation. In Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017.
X. Hua, H. Xu, J. Blanchet, and V. A. Nguyen. Human imperceptible attacks and applications to improve fairness. In 2022 Winter Simulation Conference (WSC), pages 2641-2652, 2022.
R. Huang, J. Huang, W. Liu, and H. Ding. Coresets for Wasserstein distributionally robust optimization problems. In Advances in Neural Information Processing Systems, Oct. 2022.
A. Ilyas, L. Engstrom, A. Athalye, and J. Lin. Black-box adversarial attacks with limited queries and information. In Proceedings of the 35th International Conference on Machine Learning, pages 2137-2146. PMLR, July 2018.
F. H. Knight. Risk, Uncertainty and Profit. Boston, New York, Houghton Mifflin Company, 1921.
A. Krizhevsky. Learning multiple layers of features from tiny images. 2009.
H. Lam. Robust sensitivity analysis for stochastic systems. Mathematics of OR, 41(4):1248-1275, Nov. 2016.
M. Larsson, J. Park, and J. Wiesel. On concentration of the empirical measure for general transport costs, 2023.
J. Lee and M. Raginsky. Minimax statistical learning with Wasserstein distances. Advances in Neural Information Processing Systems, 31, 2018.
L. Li, T. Xie, and B. Li. SoK: Certified robustness for deep neural networks. In 44th IEEE Symposium on Security and Privacy. IEEE, 2023.
A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu. Towards deep learning models resistant to adversarial attacks. In International Conference on Learning Representations, 2018.
P. Mohajerin Esfahani and D. Kuhn. Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Program., 171(1): 115-166, Sept. 2018.
J. L. M. Olea, C. Rush, A. Velez, and J. Wiesel. The out-of-sample prediction error of the square-root-lasso and related estimators, 2023.
T. Pang, M. Lin, X. Yang, J. Zhu, and S. Yan. Robustness and accuracy could be reconcilable by (proper) definition. In Proceedings of the 39th International Conference on Machine Learning, pages 17258-17277. PMLR, June 2022.
A. Raghunathan, J. Steinhardt, and P. S. Liang. Semidefinite relaxations for certifying robustness to adversarial examples. In Advances in Neural Information Processing Systems, volume 31. Curran Associates, Inc., 2018.
H. Rahimian and S. Mehrotra. Distributionally robust optimization: A review, Aug. 2019.