On constraint sampling in the linear programming approach to approximate dynamic programming

Mathematics of Operations Research

Volumn 29, Issue 3, 2004, Pages 462-478

  de Farias, Daniela Pucci ^a   Van Roy, Benjamin ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Basis functions; Markov decision processes; Policy; Value function

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; DECISION THEORY; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; MARKOV PROCESSES; QUEUEING NETWORKS; SAMPLING; VALUE ENGINEERING;

BASIS FUNCTION; MARKOV DECISION PROCESSES; OPTIMAL POLICY; VALUE FUNCTION;

OPERATIONS RESEARCH;

EID: 5544258192     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.1040.0094     Document Type: Article

References (14)

1. Anthony, D., N. Biggs. 1992. Computational Learning Theory. Cambridge University Press, Cambridge, UK, 95.
2. Bertsekas, D., J. N. Tsitsiklis. 1996. Neuro-Dynamic Programming. Athena Scientific, Belmont, MA.
3. Calafiore, G., M. Campi. 2003. Uncertain convex programs: Randomized solutions and confidence levels. Preprint.
4. Clarkson, K. L. 1995. Las Vegas algorithms for linear and integer programming when the dimension is small. J. Assoc. Comput. Machinery 42(2) 488-499.
5. de Farias, D. P., B. Van Roy. 2003. The linear programming approach to approximate dynamic programming. Oper. Res. 51(6) 850-865.
6. Dudley, R. M. 1978. Central limit theorems for empirical measures. Ann. Probab. 6(6) 899-929.
7. Grötschel, M., O. Holland. 1991. Solution of large-scale symmetric travelling salesman problems. Math. Programming 51 141-202.
8. Guestrin, C., D. Koller, R. Parr. 2003. Efficient solution algorithms for factored MDPs. J. Artificial Intelligence Res. 19 399-468.
9. Haussler, D., M. Kearns, N. Littlestone, M. K. Warmuth. 1991. Equivalence of models for polynomial learnability. Inform. Comput. 95(2) 129-161.
10. Morrison, J. R., P. R. Kumar. 1999. New linear program performance bounds for queueing networks. J. Optim. Theory Appl. 100(3) 575-597.
11. Schuurmans, D., R. Patrascu. 2002. Direct value-approximation for factored MDPs. Proc. 2001 Neural Inform. Processing Systems (NIPS) Conf., Adv. Neural Inform. Processing Systems, Vol. 14. MIT Press, Cambridge, MA.
12. Schweitzer, P., A. Seidmann. 1985. Generalized polynomial approximations in Markovian decision processes. J. Math. Anal. Appl. 110 568-582.
13. Trick, M., S. Zin. 1993. A linear programming approach to solving stochastic dynamic programs. Unpublished manuscript.
14. Trick, M., S. Zin. 1997. Spline approximations to value functions: A linear programming approach. Macroeconomic Dynam. 1 255-277.