Scenario Trees and Policy Selection for Multistage Stochastic Programming Using Machine Learning

Published Online:https://doi.org/10.1287/ijoc.1120.0516

References

  • Abbeel P, Ng A. Apprenticeship learning via inverse reinforcement learning. Proc. 21st Internat. Conf. Machine Learn. (ICML 2004) (2004) (ACM, New York) 1–8CrossrefGoogle Scholar
  • Bertsekas DP. Dynamic Programming and Optimal Control (2005) 3rd ed.(Athena Scientific, Belmont, MA) Google Scholar
  • Berstsekas DP, Tsitsiklis J. Neuro-Dynamic Programming (1996) (Athena Scientific, Belmont, MA) Google Scholar
  • Birge JR. State-of-the-art-survey—Stochastic programming: Computation and applications. INFORMS J. Comp. (1997) 9(2):111–133LinkGoogle Scholar
  • Birge JR, Louveaux F. Introduction to Stochastic Programming (1997) (Springer, New York) Google Scholar
  • Busoniu L, Babuska R, De Schutter B, Ernst D. Reinforcement Learning and Dynamic Programming Using Function Approximators (2010) (CRC Press, Boca Raton, FL) CrossrefGoogle Scholar
  • Chiralaksanakul A. Monte Carlo methods for multi-stage stochastic programs. (2003) . Ph.D. thesis, University of Texas at Austin, AustinGoogle Scholar
  • Coates A, Abbeel P, Ng A. Learning for control from multiple demonstrations. Proc. 25th Internat. Conf. on Machine Learn. (ICML 2008) (2008) (ACM, New York) 144–151CrossrefGoogle Scholar
  • Defourny B. Machine learning solution methods for multistage stochastic programming. (2010) . Ph.D. thesis, University of Liège, Liège, BelgiumGoogle Scholar
  • Defourny B, Ernst D, Wehenkel L. Bounds for multistage stochastic programs using supervised learning strategies. Proc. 5th internat. Conf. Stochastic Algorithms: Foundations and Applications (SAGA 2009), Vol. 5792 (2009) (Springer-Verlag, Berlin) 61–73Lecture Notes in Computer ScienceCrossrefGoogle Scholar
  • Defourny B, Ernst D, Wehenkel L, Morales EF, Sucar LE, Hoey J. Multistage stochastic programming: A scenario tree based approach to planning under uncertainty. Decision Theory Models for Applications in Artificial Intelligence: Concepts and Solutions (2012) (IGI Global, Hershey, PA) 97–143CrossrefGoogle Scholar
  • Dempster MAH, Pflug G, Mitra G. Quantitative Fund Management (2008) (Chapman & Hall/CRC, Boca Raton, FL) Financial Math. SeriesCrossrefGoogle Scholar
  • Dupacova J, Consigli G, Wallace SW. Scenarios for multistage stochastic programs. Ann. Oper. Res. (2000) 100(1–4):25–53CrossrefGoogle Scholar
  • Frauendorfer K. Barycentric scenario trees in convex multistage stochastic programming. Math. Programming (1996) 75(2):277–294CrossrefGoogle Scholar
  • Grant M, Boyd S, Blondel V, Boyd S, Kimura H. Graph implementations for nonsmooth convex programs. Recent Advances in Learning and Control—A Tribute to M. Vidyasagar (2008) (Springer, New York) 95–110Lecture Notes in Control and Information Systems, Vol. 371CrossrefGoogle Scholar
  • Grant M, Boyd S. CVX: Matlab software for disciplined convex programming (Web page and software). (2009) . Accessed February 28, 2009 http://cvxr.com/cvx/Google Scholar
  • Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2009) 2nd ed.(Springer, New York) CrossrefGoogle Scholar
  • Heitsch H, Römisch W. Scenario tree modeling for multistage stochastic programs. Math. Programming (2009) 118(2):371–406CrossrefGoogle Scholar
  • Heitsch H, Römisch W, Infanger G. Stability and scenario trees for multistage stochastic programs. Stochastic Programming—The State of the Art, In Honor of George B. Dantzig (2011) (Springer, New York) 139–164Google Scholar
  • Hilli P, Pennanen T. Numerical study of discretizations of multistage stochastic programs. Kybernetika (2008) 44(2):185–204Google Scholar
  • Høyland K, Wallace SW. Generating scenario trees for multistage decision problems. Management Sci. (2001) 47(2):295–307LinkGoogle Scholar
  • Huang K, Ahmed S. The value of multistage stochastic programming in capacity planning under uncertainty. Oper. Res. (2009) 57(4):893–904LinkGoogle Scholar
  • Kallrath J, Pardalos PM, Rebennack S, Scheidt M. Optimization in the Energy Industry (2009) (Springer-Verlag, Berlin) CrossrefGoogle Scholar
  • Kouwenberg R. Scenario generation and stochastic programming models for asset liability management. Eur. J. Oper. Res. (2001) 134(2):279–292CrossrefGoogle Scholar
  • Küchler C, Vigerske S. Numerical evaluation of approximation methods in stochastic programming. Optimization (2010) 59(3):401–415CrossrefGoogle Scholar
  • Mak W-K, Morton DP, Wood RK. Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Let. (1999) 24(1–2):47–56CrossrefGoogle Scholar
  • Mulvey JM, Kim WC, Infanger G. Multistage financial planning models: Integrating stochastic programs and policy simulators. Stochastic Programming—The State of the Art, In Honor of George B. Dantzig (2011) (Springer, New York) 257–276Google Scholar
  • Nesterov Y, Vial J-P. Confidence level solutions for stochastic programming. Automatica (2008) 44(6):1559–1568CrossrefGoogle Scholar
  • O'Hagan A. Curve fitting and optimal design for prediction. J. Roy. Statist. Soc. (1978) 40(1):1–42Google Scholar
  • Pages G, Printems J. Optimal quadratic quantization for numerics: The Gaussian case. Monte Carlo Methods Appl. (2003) 9(2):135–166CrossrefGoogle Scholar
  • Pennanen T. Epi-convergent discretizations of multistage stochastic programs. Math. Oper. Res. (2005) 30(1):245–256LinkGoogle Scholar
  • Pennanen T. Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Math. Programming (2009) 116(1):461–479CrossrefGoogle Scholar
  • Peters J, Schaal S. Natural actor-critic. Neurocomputing (2008) 71(7–9):1180–1190CrossrefGoogle Scholar
  • Powell WB. Approximate Dynamic Programming: Solving the Curses of Dimensionality (2011) 2nd ed.(Wiley, Hoboken, NJ) CrossrefGoogle Scholar
  • Rasmussen CE, Williams CKI. Gaussian Processes for Machine Learning (2006) (MIT Press, Cambridge, MA) Google Scholar
  • Rockafellar RT, Wets RJ-B. Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. (1991) 16(1):119–147LinkGoogle Scholar
  • Shapiro A. Inference of statistical bounds for multistage stochastic programming problems. Math. Methods Oper. Res. (2003) 58(1):57–68CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczyński A. Lectures on Stochastic Programming: Modeling and Theory (2009) (SIAM, Philadelphia) MPS-SIAM Series on OptimizationCrossrefGoogle Scholar
  • Sutton RS, Barto AG. Reinforcement Learning, an Introduction (1998) (MIT Press, Cambridge, MA) CrossrefGoogle Scholar
  • Syed U, Bowling M, Schapire RE. Apprenticeship learning using linear programming. Proc. 25th Internat. Conf. Machine Learn. (ICML 2008) (2008) (Omni Press, Madison, WI) 1032–1039CrossrefGoogle Scholar
  • Szepesvári C. Algorithms for Reinforcement Learning (2010) (Morgan & Claypool Publishers)CrossrefGoogle Scholar
  • Thénié J, Vial J-P. Step decision rules for multistage stochastic programming: A heuristic approach. Automatica (2008) 44(6):1569–1584CrossrefGoogle Scholar
  • Wallace SW, Ziemba WT. Applications of Stochastic Programming (2005) (SIAM, Philadelphia) MPS-SIAM Series on OptimizationCrossrefGoogle 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.