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Robust Markov Decision Processes

Author

Listed:
  • Wolfram Wiesemann
  • Daniel Kuhn
  • Berç Rustem

Abstract

Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider robust MDPs that offer probabilistic guarantees in view of the unknown parameters. To this end, we assume that an observation history of the MDP is available. Based on this history, we derive a confidence region that contains the unknown parameters with a pre-specified probability 1-ß. Afterwards, we determine a policy that attains the highest worst-case performance over this confidence region. By construction, this policy achieves or exceeds its worst-case performance with a confidence of at least 1 - ß. Our method involves the solution of tractable conic programs of moderate size.

Suggested Citation

  • Wolfram Wiesemann & Daniel Kuhn & Berç Rustem, 2010. "Robust Markov Decision Processes," Working Papers 034, COMISEF.
    • Handle: RePEc:com:wpaper:034
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    References listed on IDEAS

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    1. Jay K. Satia & Roy E. Lave, 1973. "Markovian Decision Processes with Uncertain Transition Probabilities," Operations Research, INFORMS, vol. 21(3), pages 728-740, June.
    2. Shie Mannor & Duncan Simester & Peng Sun & John N. Tsitsiklis, 2007. "Bias and Variance Approximation in Value Function Estimates," Management Science, INFORMS, vol. 53(2), pages 308-322, February.
    3. Chelsea C. White & Hany K. Eldeib, 1994. "Markov Decision Processes with Imprecise Transition Probabilities," Operations Research, INFORMS, vol. 42(4), pages 739-749, August.
    4. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
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