Data-Driven Minimax Optimization with Expectation Constraints

References

• Ben-Tal A, Nemirovski A (2002) Robust optimization: Methodology and applications. Math. Programming 92(3):453–480.Crossref, Google Scholar
• Ben-Tal A, Nemirovski A (2003) On approximate robust counterparts of uncertain semidefinite and conic quadratic programs. Sachs EW, Tichatschke R, eds. System Modeling and Optimization XX. CSMO 2001. IFIP — The International Federation for Information Processing, vol. 130 (Springer, Berlin), 1–22.Google Scholar
• Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Bertsekas D (1999) Nonlinear Programming, 2nd ed. (Athena Scientific, Belmont, MA).Google Scholar
• Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math. Programming 98(1):49–71.Crossref, Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Boob D, Deng Q, Lan G (2023) Stochastic first-order methods for convex and nonconvex functional constrained optimization. Math. Programming 197(1):215–279.Crossref, Google Scholar
• Chambolle A, Pock T (2011) A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vision 40(1):120–145.Crossref, Google Scholar
• Chen Y, Lan G, Ouyang Y (2014) Optimal primal-dual methods for a class of saddle point problems. SIAM J. Optim. 24(4):1779–1814.Crossref, Google Scholar
• Chen Y, Lan G, Ouyang Y (2017) Accelerated schemes for a class of variational inequalities. Math. Programming 165(1):113–149.Crossref, Google Scholar
• Danskin JM (2012) The Theory of Max-Min and Its Application to Weapons Allocation Problems, vol. 5 (Springer Science & Business Media, Boston).Google Scholar
• Dempe S (2002) Foundations of Bilevel Programming (Springer Science & Business Media, Boston).Google Scholar
• Dempe S, Zemkoho AB (2013) The bilevel programming problem: Reformulations, constraint qualifications and optimality conditions. Math. Programming 138(1):447–473.Crossref, Google Scholar
• Di Liello L, Ardino P, Gobbi J, Morettin P, Teso S, Passerini A (2020) Efficient generation of structured objects with constrained adversarial networks. Adv. Neural Inform. Process. Systems 33:14663–14674.Google Scholar
• Dua D, Graff C (2017) UCI machine learning repository. Accessed November 16, 2021, http://archive.ics.uci.edu/ml.Google Scholar
• Fan J, Han F, Liu H (2014) Challenges of big data analysis. National Sci. Rev. 1(2):293–314.Crossref, Google Scholar
• Gallego G, Topaloglu H (2019) Revenue Management and Pricing Analytics, vol. 209 (Springer, Berlin).Crossref, Google Scholar
• Ghosh S, Sahare M, Mukhoti S (2021) A new generalized newsvendor model with random demand and cost misspecification. Strategic Management, Decision Theory, and Decision Science (Springer, Berlin), 211–245.Crossref, Google Scholar
• Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville AC, Bengio Y (2014) Generative adversarial nets. Adv. Neural Inform. Process. Systems 27:2672–2680.Google Scholar
• Grant M, Boyd S (2014) CVX: Matlab software for disciplined convex programming, version 2.1. Accessed November 20, 2021, http://cvxr.com/cvx.Google Scholar
• Hamedani EY, Aybat NS (2021) A primal-dual algorithm with line search for general convex-concave saddle point problems. SIAM J. Optim. 31(2):1299–1329.Crossref, Google Scholar
• Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (roc) curve. Radiology 143(1):29–36.Crossref, Google Scholar
• He N, Juditsky A, Nemirovski A (2015) Mirror prox algorithm for multi-term composite minimization and semi-separable problems. Comput. Optim. Appl. 61(2):275–319.Crossref, Google Scholar
• Heim E (2019) Constrained generative adversarial networks for interactive image generation. Proc. IEEE/CVF Conf. on Computer Vision and Pattern Recognition, 10753–10761.Google Scholar
• Jiang H, Shanbhag UV (2013) On the solution of stochastic optimization problems in imperfect information regimes. Proc. Winter Simulation Conf., 821–832.Google Scholar
• Jiang H, Shanbhag UV (2016) On the solution of stochastic optimization and variational problems in imperfect information regimes. SIAM J. Optim. 26(4):2394–2429.Crossref, Google Scholar
• Lan G (2020) First-Order and Stochastic Optimization Methods for Machine Learning (Springer Nature, Berlin).Crossref, Google Scholar
• Lan G, Zhou Z (2020) Algorithms for stochastic optimization with functional or expectation constraints. Comput. Optim. Appl. 76:461–498.Crossref, Google Scholar
• Lan G, Romeijn E, Zhou Z (2021) Conditional gradient methods for convex optimization with general affine and nonlinear constraints. SIAM J. Optim. 31(3):2307–2339.Crossref, Google Scholar
• Lemaréchal C, Nemirovskii A, Nesterov Y (1995) New variants of bundle methods. Math. Programming 69(1):111–147.Crossref, Google Scholar
• Lin Q, Nadarajah S, Soheili N, Yang T (2020) A data efficient and feasible level set method for stochastic convex optimization with expectation constraints. J. Machine Learn. Res. 21(143):1–45.Google Scholar
• Loridan P, Morgan J (1996) Weak via strong Stackelberg problem: New results. J. Global Optim. 8(3):263–287.Crossref, Google Scholar
• Mitsos A, Lemonidis P, Barton PI (2008) Global solution of bilevel programs with a nonconvex inner program. J. Global Optim. 42(4):475–513.Crossref, Google Scholar
• Myerson RB (1997) Game Theory: Analysis of Conflict (Harvard University Press, Cambridge, MA).Google Scholar
• Nemirovski A (1994) Information-based complexity of convex programming. Lecture notes, https://www2.isye.gatech.edu/~nemirovs/LecEMCO.pdf.Google Scholar
• Nemirovski A (2004) Prox-method with rate of convergence o(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J. Optim. 15(1):229–251.Crossref, Google Scholar
• Nemirovsky A, Yudin D (1983) Problem Complexity and Method Efficiency in Optimization (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Nemirovski A, Juditsky A, Lan G, Shapiro A (2009) Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4):1574–1609.Crossref, Google Scholar
• Nesterov Y (2003) Introductory Lectures on Convex Programming volume i: Basic course. Applied Optimization, vol. 87 (Kluwer Academic, Dordrecht, Netherlands).Google Scholar
• Nesterov Y (2005) Smooth minimization of non-smooth functions. Math. Programming 103(1):127–152.Crossref, Google Scholar
• Nouiehed M, Sanjabi M, Huang T, Lee JD, Razaviyayn M (2019) Solving a class of non-convex min-max games using iterative first order methods. Adv. Neural Inform. Processing Systems 32:14905–14916.Google Scholar
• Oliveira RI, Thompson P (2023a) Sample average approximation with heavier tails I: Non-asymptotic bounds with weak assumptions and stochastic constraints. Math. Programming 199(1–2):1–48.Crossref, Google Scholar
• Oliveira RI, Thompson P (2023b) Sample average approximation with heavier tails II: Localization in stochastic convex optimization and persistence results for the Lasso. Math. Programming 199(1–2):49–86.Crossref, Google Scholar
• Outrata JV (1988) A note on the usage of nondifferentiable exact penalties in some special optimization problems. Kybernetika (Prague) 24(4):251–258.Google Scholar
• Ouyang Y, Xu Y (2021) Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems. Math. Programming 185(1–2):1–35.Crossref, Google Scholar
• Pearsall ES (1976) A Lagrange multiplier method for certain constrained min-max problems. Oper. Res. 24(1):70–91.Link, Google Scholar
• Shapiro A (2013) Sample average approximation. Encyclopedia Oper. Res. Management Sci. 3:1350–1355.Crossref, Google Scholar
• Soland RM (1973) Optimal defensive missile allocation: A discrete min-max problem. Oper. Res. 21(2):590–596.Link, Google Scholar
• Von Neumann J, Morgenstern O (2007) Theory of Games and Economic Behavior (Princeton University Press, Princeton, NJ).Google Scholar
• Wiesemann W, Tsoukalas A, Kleniati PM, Rustem B (2013) Pessimistic bilevel optimization. SIAM J. Optim. 23(1):353–380.Crossref, Google Scholar
• Ying Y, Wen L, Lyu S (2016) Stochastic online AUC maximization. Adv. Neural Inform. Processing Systems 29:451–459.Google Scholar
• Yu H, Neely M, Wei X (2017) Online convex optimization with stochastic constraints. Adv. Neural Inform. Processing Systems 30:1428–1438.Google Scholar
• Zafar MB, Valera I, Gomez-Rodriguez M, Gummadi KP (2019) Fairness constraints: A flexible approach for fair classification. J. Machine Learn. Res. 20(1):2737–2778.Google Scholar
• Zhang Z, Lan G (2022) Solving convex smooth function constrained optimization is as almost easy as unconstrained optimization. Preprint, submitted October 11, https://arxiv.org/abs/2210.05807.Google Scholar
• Zhang L, Zhang Y, Xiao X, Wu J (2023) Stochastic approximation proximal method of multipliers for convex stochastic programming. Math. Oper. Res. 48(1):177–193.Link, Google Scholar