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The Linear Programming Approach to Approximate Dynamic Programming

Author

Listed:
  • D. P. de Farias

    (Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • B. Van Roy

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94306)

Abstract

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits” a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and “state-relevance weights” that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.

Suggested Citation

  • D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:6:p:850-865
    DOI: 10.1287/opre.51.6.850.24925
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    References listed on IDEAS

    as
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    7. D. P. De Farias & B. Van Roy, 2000. "On the Existence of Fixed Points for Approximate Value Iteration and Temporal-Difference Learning," Journal of Optimization Theory and Applications, Springer, vol. 105(3), pages 589-608, June.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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