Data-Driven Distributionally Robust Optimization over Time

References

• Altın A, Amaldi E, Belotti P, Pınar MÇ (2007) Provisioning virtual private networks under traffic uncertainty. Networks 49(1):100–115.Google Scholar
• Bärmann A, Pokutta S, Schneider O (2017) Emulating the Expert: Inverse Optimization Through Online Learning. ICML (PMLR, San Diego), 400–410.Google Scholar
• Bärmann A, Martin A, Pokutta S, Schneider O (2018) An online-learning approach to inverse optimization. Preprint, submitted October 30, https://arxiv.org/abs/1810.12997.Google Scholar
• Bayraksan G, Love DK (2015) Data-Driven Stochastic Programming Using Phi-Divergences. The Operations Research Revolution (INFORMS, Catonsville), 1–19.Google Scholar
• Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton).Google Scholar
• Ben-Tal A, Hazan E, Koren T, Mannor S (2015) Oracle-based robust optimization via online learning. Oper. Res. 63(3):628–638.Link, Google Scholar
• Bertsimas D, Gupta V, Kallus N (2018) Data-driven robust optimization. Math. Programming 167(2):235–292.Google Scholar
• Besbes O, Gur Y, Zeevi A (2015) Non-stationary stochastic optimization. Oper. Res. 63(5):1227–1244.Link, Google Scholar
• Birge JR, Louveaux F (1997) Introduction to Stochastic Programming. Springer Series in Operations Research (Springer, New York).Google Scholar
• Cacchiani V, Jünger M, Liers F, Lodi A, Schmidt D (2016) Single-commodity robust network design with finite and hose demand sets. Math. Programming 157(1):297–342.Google Scholar
• Calafiore GC, Ghaoui LE (2006) On distributionally robust chance-constrained linear programs. J. Optim. Theory App. 130(1):1–22.Google Scholar
• Chen RS, Lucier B, Singer Y, Syrgkanis V (2017) Robust optimization for non-convex objectives. Adv. NeurIPS. 30:4708–4717.Google Scholar
• Chen Z, Sim M, Xiong P (2020) Robust stochastic optimization made easy with rsome. Management Sci. 66(8):3329–3339.Link, 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.Link, Google Scholar
• Duchi JC, Glynn PW, Namkoong H (2021) Statistics of robust optimization: A generalized empirical likelihood approach. Math. Oper. Res. 46(3):946–969.Link, 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.Google Scholar
• Fitzpatrick S, Scott A (1987) Quick simultaneous confidence intervals for multinomial proportions. J. Amer. Statist. Assoc. 82(399):875–878.Google Scholar
• Furini F, Traversi E, Belotti P, Frangioni A, Gleixner A, Gould N, Liberti L, et al. (2019) Qplib: A library of quadratic programming instances. Math. Programming Comp. 11(2):237–265.Google Scholar
• Gamrath G, Anderson D, Bestuzheva K, Chen WK, Eifler L, Gasse M, Gemander P, et al. (2020) The SCIP Optimization Suite 7.0. ZIB-Report 20-10, Zuse Institute Berlin, http://nbn-resolving.de/urn:nbn:de:0297-zib-78023.Google Scholar
• Ghayoori A, Leon-Garcia A (2013) Robust network design. 2013 IEEE Inter. Conf. Comm. (ICC), 2409–2414 (IEEE, Piscataway, NJ).Google Scholar
• Gleixner A, Hendel G, Gamrath G, Achterberg T, Bastubbe M, Berthold T, Christophel P, et al. (2021) Miplib 2017: Data-driven compilation of the 6th mixed-integer programming library. Math. Prog. Comp. 13(3):443–490.Google Scholar
• Hanasusanto GA, Roitch V, Kuhn D, Wiesemann W (2015) A distributionally robust perspective on uncertainty quantification and chance constrained programming. Math. Programming 151(1):35–62.Google Scholar
• Hazan E (2016) Introduction to online convex optimization. Found. Trends Optim. 2(3–4):41–54.Google Scholar
• Heidt A, Helmke H, Kapolke M, Liers F, Martin A (2016) Robust runway scheduling under uncertain conditions. Journal of Air Transport Management 56(PA):28–37.Google Scholar
• Ho-Nguyen N, Kılınç-Karzan F (2018) Online first-order framework for robust convex optimization. Oper. Res. 66(6):1670–1692.Link, Google Scholar
• Husain H, Nguyen V, van den Hengel A (2022) Distributionally robust bayesian optimization with ϕ-divergences. Preprint, submitted March 4, https://arxiv.org/abs/2203.02128.Google Scholar
• Kapolke M, Fürstenau N, Heidt A, Liers F, Mittendorf M, Weiß C (2016) Pre-tactical optimization of runway utilization under uncertainty. J. Air Transp. Management 56(PA):48–56.Google Scholar
• Kirschner J, Bogunovic I, Jegelka S, Krause A (2020) Distributionally robust bayesian optimization. Inter. Conf. on Artif. Intel. and Stat. (PMLR), 2174–2184.Google Scholar
• Kleywegt AJ, Shapiro A, Homem-de Mello T (2002) The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12(2):479–502.Google Scholar
• Levy D, Carmon Y, Duchi JC, Sidford A (2020) Large-scale methods for distributionally robust optimization. Adv. NeurIPS. 33:8847–8860.Google Scholar
• Mokhtari A, Shahrampour S, Jadbabaie A, Ribeiro A (2016) Online optimization in dynamic environments: Improved regret rates for strongly convex problems. 2016 IEEE 55th Conference on Decision and Control (IEEE, Piscataway, NJ), 7195–7201.Google Scholar
• Namkoong H, Duchi JC (2016) Stochastic gradient methods for distributionally robust optimization with f-divergences. Adv. NeurIPS. 29:2208–2216.Google Scholar
• Pokutta S, Xu H (2021) Adversaries in online learning revisited: With applications in robust optimization and adversarial training. Preprint, submitted January 27, https://arxiv.org/abs/2101.11443.Google Scholar
• Qi Q, Guo Z, Xu Y, Jin R, Yang T (2021) An online method for a class of distributionally robust optimization with non-convex objectives. Adv. NeurIPS. 34:10067–10080.Google Scholar
• Rahimian H, Mehrotra S (2019) Distributionally robust optimization: A review. Preprint, submitted August 13, https://arxiv.org/abs/1908.05659.Google Scholar
• Sessa PG, Bogunovic I, Kamgarpour M, Krause A (2020) Mixed strategies for robust optimization of unknown objectives. Inter. Conf. on Artif. Intel. and Stat. (PMLR), 2970–2980.Google Scholar
• Stabler B, Bar-Gera H, Sall E (2018) Transportation networks for research. Accessed April 12, 2023, https://github.com/bstabler/TransportationNetworks.Google Scholar
• Van Parys BP, Esfahani PM, Kuhn D (2021) From data to decisions: Distributionally robust optimization is optimal. Management Sci. 67(6):3387–3402.Link, Google Scholar
• Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programming 106(1):25–57.Google Scholar
• Wang H (2008) Exact confidence coefficients of simultaneous confidence intervals for multinomial proportions. J. Multivariate Anal. 99(5):896–911.Google Scholar
• Weissman T, Ordentlich E, Seroussi G, Verdu S, Weinberger MJ (2003) Inequalities for the l1 Deviation of the Empirical Distribution (Hewlett-Packard Labs, Tech. Rep, Princeton, NJ).Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Zhao P, Zhang YJ, Zhang L, Zhou ZH (2020) Dynamic regret of convex and smooth functions. Adv. NeurIPS. 33:12510–12520.Google Scholar
• Zinkevich M (2003) Online convex programming and generalized infinitesimal gradient ascent. ICML, 928–936.Google Scholar