Data-Driven Optimization: A Reproducing Kernel Hilbert Space Approach

References

• Aronszajn N (1950) Theory of reproducing kernels. Trans. Amer. Math. Soc. 68:337–404.Crossref, Google Scholar
• Ban GY, Rudin C (2019) The big data newsvendor: Practical insights from machine learning. Oper. Res. 67(1):90–108.Link, Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Bertsimas D, Kallus N (2020) From predictive to prescriptive analytics. Management Sci. 66(3):1025–1044.Link, Google Scholar
• Bertsimas D, McCord C (2019) From predictions to prescriptions in multistage optimization problems. Preprint, submitted. April 26, https://arxiv.org/abs/1904.11637.Google Scholar
• Bertsimas D, Tsitsiklis JN (1997) Introduction to Linear Optimization (Athena Scientific, Belmont, MA).Google Scholar
• Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464–501.Crossref, Google Scholar
• Bertsimas D, Gupta V, Kallus N (2018) Data-driven robust optimization. Math. Programming 167(2):235–292.Crossref, Google Scholar
• Birge JR, Louveaux F (2011) Introduction to Stochastic Programming (Springer, New York).Crossref, Google Scholar
• Bousquet O, Elisseeff A (2002) Stability and generalization. J. Machine Learn. Res. 2:499–526.Google Scholar
• Cucker F, Smale S (2002) On the mathematical foundations of learning. Bull. Amer. Math. Soc. 39(1):1–49.Google Scholar
• Delage E, Ye YY (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Google Scholar
• Hanasusanto GA, Kuhn D (2013) Robust data-driven dynamic programming. Adv. Neural Inform. Processing Systems 26:827–835.Google Scholar
• Hannah L, Powell WB, Blei DM (2010) Nonparametric density estimation for stochastic optimization with an observable state variable. Adv. Neural Inform. Processing Systems 23:820–828.Google Scholar
• Hastie T, Tibshirani R, Friedman J (2009) The Elements of Statistical Learning, 2nd ed. (Springer-Verlag, New York).Crossref, 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
• Micchelli CA, Xu Y, Zhang H (2006) Universal kernels. J. Machine Learn. Res. 7:2651–2667.Google Scholar
• Mohri M, Rostamizadeh A, Talwalkar A (2018) Foundations of Machine Learning, 2nd ed. (MIT Press, Cambridge, Massachusetts).Google Scholar
• Oneto L, Ridella S, Anguita D (2016) Tikhonov, Ivanov and Morozov regularization for support vector machine learning. Machine Learn. 103:103–136.Crossref, Google Scholar
• Poggio T, Smale S (2003) The mathematics of learning: Dealing with data. Notices AMS 50(5):537–544.Google Scholar
• Shapiro A (2003) Monte Carlo sampling methods. Ruszczynski A, Shapiro A, eds. Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, Amsterdam), 353–425.Google Scholar
• Shapiro A, Nemirovski A (2005) On complexity of stochastic programming problems.Jeyakumar V, Rubinov A, eds. Continuous Optimization, vol. 99 (Springer, Boston), 111–146.Crossref, Google Scholar
• Vapnik VN (1998) Statistical Learning Theory, 1st ed. (John Wiley & Sons, New York).Google Scholar