The Linear Programming Approach to Approximate Dynamic Programming

References

• Bertsekas D.Dynamic Programming and Optimal Control (1995) (Athena Scientific, Belmont, MA) Google Scholar
• Bertsekas D., Tsitsiklis J. N.Neuro-Dynamic Programming (1996) (Athena Scientific, Belmont, MA) Google Scholar
• Bertsekas D., Gamarnik D., Tsitsiklis J. Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions. Ann. Appl. Probab. (2001) 11(4):1384–1428Crossref, Google Scholar
• Bishop C. M.Neural Networks for Pattern Recognition (1995) (Oxford University Press, New York) Crossref, Google Scholar
• Borkar V. A convex analytic approach to Markov decision processes. Probab. Theory Related Fields (1988) 78:583–602Crossref, Google Scholar
• Chen R.-R., Meyn S. Value iteration and optimization of multiclass queueing networks. Queueing Systems (1999) 32:65–97Crossref, Google Scholar
• Chen V. C. P., Ruppert D., Shoemaker C. A. Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming. Oper. Res. (1999) 47(1):38–53Link, Google Scholar
• Crites R. H., Barto A. G. Improving elevator performance using reinforcement learning. Advances in Neural Information Processing Systems (1996) 8(MIT Press, Cambridge, MA) 1017–1023Google Scholar
• Dayan P. The convergence of TD(λ) for general λ. Machine Learning (1992) 8:341–362Crossref, Google Scholar
• de Farias D. P., Van Roy B. On the existence of fixed points for appproximate value iteration and temporal-difference learning. J. Optim. Theory Appl. (2000) 105(3):589–608Crossref, Google Scholar
• de Farias D. P., Van Roy B. On constraint sampling in the linear programming approach to approximate dynamic programming. Math. Oper. Res. (2001) . Conditionally accepted toGoogle Scholar
• De Ghellinck G. Les problèmes de décisions séquentielles. Cahiers du Centre d'Etudes de Recherche Opérationnelle (1960) 2:161–179Google Scholar
• Denardo E. V. On linear programming in a Markov decision problem. Management Sci. (1970) 16(5):282–288Link, Google Scholar
• D'Epenoux F. A probabilistic production and inventory problem. Management Sci. (1963) 10(1):98–108Link, Google Scholar
• Gordon G. Approximate solutions to Markov decision processess. (1999) . Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PAGoogle Scholar
• Grötschel M., Holland O. Solution of large-scale symmetric travelling salesman problems. Math. Programming (1991) 51:141–202Crossref, Google Scholar
• Guestrin C., Koller D., Parr R. Efficient solution algorithms for factored MDPs. J. Artificial Intelligence Res. (2002) . ForthcomingGoogle Scholar
• Haykin S.Neural Networks: A Comprehensive Formulation (1994) (Macmillan, New York) Google Scholar
• Hordijk A., Kallenberg L. C. M. Linear programming and Markov decision chains. Management Sci. (1979) 25:352–362Link, Google Scholar
• Kumar P. R., Seidman T. I. Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems. IEEE Trans. Automatic Control (1990) 35(3):289–298Crossref, Google Scholar
• Longstaff F., Schwartz E. S. Valuing American options by simulation: A simple least squares approach. Rev. Financial Stud. (2001) 14:113–147Crossref, Google Scholar
• Manne A. S. Linear programming and sequential decisions. Management Sci. (1960) 6(3):259–267Link, Google Scholar
• Morrison J. R., Kumar P. R. New linear program performance bounds for queueing networks. J. Optim. Theory Appl. (1999) 100(3):575–597Crossref, Google Scholar
• Paschalidis I. C., Tsitsiklis J. N. Congestion-dependent pricing of network services. IEEE/ACM Trans. Networking (2000) 8(2):171–184Crossref, Google Scholar
• Rybko A. N., Stolyar A. L. On the ergodicity of stochastic processes describing the operation of open queueing networks. Problemy Peredachi Informatsii (1992) 28:3–26Google Scholar
• Schuurmans D., Patrascu R. Direct value-approximation for factored MDPs. Advances in Neural Information Processing Systems (2001) 14(MIT Press, Cambridge, MA) 1579–1586Google Scholar
• Schweitzer P., Seidmann A. Generalized polynomial approximations in Markovian decision processes. J. Math. Anal. Appl. (1985) 110:568–582Crossref, Google Scholar
• Sutton R. S. Learning to predict by the methods of temporal differences. Machine Learning (1988) 3:9–44Crossref, Google Scholar
• Sutton R. S., Barto A. G.Reinforcement Learning: An Introduction (1998) (MIT Press, Cambridge, MA) Google Scholar
• Tesauro C. J. Temporal difference learning and TD-gammon. Comm. ACM (1995) 38:58–68Crossref, Google Scholar
• Trick M., Zin S. A linear programming approach to solving dynamic programs. (1993) . Unpublished manuscriptGoogle Scholar
• Trick M., Zin S. Spline approximations to value functions: A linear programming approach. Macroeconomic Dynamics (1997) 1:255–277Crossref, Google Scholar
• Tsitsiklis J. N., Van Roy B. An analysis of temporal-difference learning with function approximation. IEEE Trans. Auto. Control (1997) 42(5):674–690Crossref, Google Scholar
• Tsitsiklis J. N., Van Roy B. Regression methods for pricing complex American-style options. IEEE Trans. Neural Networks (2001) 12(4):694–703Crossref, Google Scholar
• Van Roy B. Learning and value function approximation in complex decision processes. (1998) . Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MAGoogle Scholar
• Van Roy B., Feinberg E., Schwartz A. Neuro-dynamic programming: Overview and recent trends. Markov Decision Processes: Models, Methods, Directions, and Open Problems (2000) (Kluwer, Norwell, MA) Google Scholar
• Zhang W., Dietterich T. G. High-performance job-shop scheduling with a time-delay TD(λ) network. Advances in Neural Information Processing Systems (1996) 8(MIT Press, Cambridge, MA) 1024–1030Google Scholar