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(Approximate) iterated successive approximations algorithm for sequential decision processes

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  • Pelin Canbolat
  • Uriel Rothblum

Abstract

The paper proves the convergence of (Approximate) Iterated Successive Approximations Algorithm for solving infinite-horizon sequential decision processes satisfying the monotone contraction assumption. At every stage of this algorithm, the value function at hand is used as a terminal reward to determine an (approximately) optimal policy for the one-period problem. This policy is then iterated for a (finite or infinite) number of times and the resulting return function is used as the starting value function for the next stage of the scheme. This method generalizes the standard successive approximations, policy iteration and Denardo’s generalization of the latter. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Pelin Canbolat & Uriel Rothblum, 2013. "(Approximate) iterated successive approximations algorithm for sequential decision processes," Annals of Operations Research, Springer, vol. 208(1), pages 309-320, September.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:309-320:10.1007/s10479-012-1073-x
    DOI: 10.1007/s10479-012-1073-x
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    References listed on IDEAS

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    1. Eric V. Denardo & Uriel G. Rothblum, 1983. "Affine Structure and Invariant Policies for Dynamic Programs," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 342-365, August.
    2. Dimitri P. Bertsekas & Huizhen Yu, 2012. "Q-Learning and Enhanced Policy Iteration in Discounted Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 66-94, February.
    3. Martin L. Puterman & Moon Chirl Shin, 1978. "Modified Policy Iteration Algorithms for Discounted Markov Decision Problems," Management Science, INFORMS, vol. 24(11), pages 1127-1137, July.
    4. Ward Whitt, 1978. "Approximations of Dynamic Programs, I," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 231-243, August.
    5. Martin L. Puterman & Moon Chirl Shin, 1982. "Action Elimination Procedures for Modified Policy Iteration Algorithms," Operations Research, INFORMS, vol. 30(2), pages 301-318, April.
    6. Haviv, Moshe, 1985. "Block-successive approximation for a discounted Markov decision model," Stochastic Processes and their Applications, Elsevier, vol. 19(1), pages 151-160, February.
    7. Evan L. Porteus, 1971. "Some Bounds for Discounted Sequential Decision Processes," Management Science, INFORMS, vol. 18(1), pages 7-11, September.
    8. Martin L. Puterman & Shelby L. Brumelle, 1979. "On the Convergence of Policy Iteration in Stationary Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 60-69, February.
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    Cited by:

    1. Abdellatif Semmouri & Mostafa Jourhmane & Zineb Belhallaj, 2020. "Discounted Markov decision processes with fuzzy costs," Annals of Operations Research, Springer, vol. 295(2), pages 769-786, December.

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