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An Adaptive Sampling Algorithm for Solving Markov Decision Processes

Author

Listed:
  • Hyeong Soo Chang

    (Department of Computer Science and Engineering, Sogang University, Seoul, Korea)

  • Michael C. Fu

    (Robert H. Smith School of Business, and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • Jiaqiao Hu

    (Department of Electrical and Computer Engineering, and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • Steven I. Marcus

    (Department of Electrical and Computer Engineering, and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

Abstract

Based on recent results for multiarmed bandit problems, we propose an adaptive sampling algorithm that approximates the optimal value of a finite-horizon Markov decision process (MDP) with finite state and action spaces. The algorithm adaptively chooses which action to sample as the sampling process proceeds and generates an asymptotically unbiased estimator, whose bias is bounded by a quantity that converges to zero at rate (ln N )/ N , where N is the total number of samples that are used per state sampled in each stage. The worst-case running-time complexity of the algorithm is O (( |A|N ) H ), independent of the size of the state space, where | A | is the size of the action space and H is the horizon length. The algorithm can be used to create an approximate receding horizon control to solve infinite-horizon MDPs. To illustrate the algorithm, computational results are reported on simple examples from inventory control.

Suggested Citation

  • Hyeong Soo Chang & Michael C. Fu & Jiaqiao Hu & Steven I. Marcus, 2005. "An Adaptive Sampling Algorithm for Solving Markov Decision Processes," Operations Research, INFORMS, vol. 53(1), pages 126-139, February.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:1:p:126-139
    DOI: 10.1287/opre.1040.0145
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    References listed on IDEAS

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    1. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
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    Cited by:

    1. Woonghee Tim Huh & Paat Rusmevichientong, 2014. "Online Sequential Optimization with Biased Gradients: Theory and Applications to Censored Demand," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 150-159, February.
    2. Mohammed Shahid Abdulla & Shalabh Bhatnagar, 2016. "Multi-armed bandits based on a variant of Simulated Annealing," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 195-212, June.
    3. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    4. Michael C. Fu, 2019. "Simulation-Based Algorithms for Markov Decision Processes: Monte Carlo Tree Search from AlphaGo to AlphaZero," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-25, December.
    5. Rishabh Gupta & Qi Zhang, 2022. "Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2720-2735, September.
    6. William L. Cooper & Bharath Rangarajan, 2012. "Performance Guarantees for Empirical Markov Decision Processes with Applications to Multiperiod Inventory Models," Operations Research, INFORMS, vol. 60(5), pages 1267-1281, October.
    7. Oleg Szehr, 2021. "Hedging of Financial Derivative Contracts via Monte Carlo Tree Search," Papers 2102.06274, arXiv.org, revised Apr 2021.
    8. Ronald Ortner, 2013. "Adaptive aggregation for reinforcement learning in average reward Markov decision processes," Annals of Operations Research, Springer, vol. 208(1), pages 321-336, September.
    9. Daniel R. Jiang & Lina Al-Kanj & Warren B. Powell, 2020. "Optimistic Monte Carlo Tree Search with Sampled Information Relaxation Dual Bounds," Operations Research, INFORMS, vol. 68(6), pages 1678-1697, November.

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