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Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models

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Abstract

We consider a discrete time Markov Decision Process (MDP) under the discounted payoff criterion in the presence of additional discounted cost constraints. We study the sensitivity of optimal Stationary Randomized (SR) policies in this setting with respect to the upper bound on the discounted cost constraint functionals. We show that such sensitivity analysis leads to an improved version of the Feinberg–Shwartz algorithm (Math Oper Res 21(4):922–945, 1996) for finding optimal policies that are ultimately stationary and deterministic.

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References

  • Altman E (1999) Constrained Markov decision processes. Chapman and Hall, Boca Raton

    MATH  Google Scholar 

  • Bertsekas DP (1995) Dynamic programming and optimal control, Vol.1 and 2. Athena Scientific, Belmont

    MATH  Google Scholar 

  • Balaji J, Hemachandra N (2005) Sensitivity analysis of (s, S) policies. Under revision

  • Chvatal V (1983) Linear programming. W.H. Freeman and Company, New York

    MATH  Google Scholar 

  • Derman C, Klein M (1965) Some remarks on finite horizon Markovian decision models. Oper Res 13: 272–278

    Article  MATH  MathSciNet  Google Scholar 

  • Feinberg EA, Shwartz A (1994) Markov decision models with weighted discounted criteria. Math Oper Res 19: 152–168

    Article  MATH  MathSciNet  Google Scholar 

  • Feinberg EA, Shwartz A (1995) Constrained Markov decision models with weighted discounted rewards. Math Oper Res 20: 302–320

    Article  MATH  MathSciNet  Google Scholar 

  • Feinberg EA, Shwartz A (1996) Constrained discounted dynamic programming. Math Oper Res 21(4): 922–945

    Article  MATH  MathSciNet  Google Scholar 

  • Feinberg EA, Shwartz A (2002) Handbook of Markov decision processes: methods and applications. Kluwer, Boston

    MATH  Google Scholar 

  • Iyer KR, Hemachandra N (2007) Ultimately stationary deterministic strategies for stochastic games. In: Proceedings of the international conference on advances in control and optimization of dynamical systems (ACODS 2007), IISc., Bangalore, Feb 1–2, pp 414–421

  • Iyer K, Hemachandra N (2006) An algorithm for some constrained optimal stopping time problems. Working Paper, IEOR, IIT Bombay

  • Jaquette SC (1976) A utility criterion for Markov decision processes. Manag Sci 23(1): 43–49

    Article  MATH  MathSciNet  Google Scholar 

  • Puranam KS, Hemachandra N (2005) Sensitivity analysis of control limit with respect to the cost parameters in an M/M/1 queue. Vision 2020: the strategic role of operational research, 2006. Based on 37th annual convention of Operational Research Society of India, IIM Ahmedabad, Jan 8–11, pp 433–439

  • Puterman ML (1994) Markov decision processes. Wiley, New York

    Book  MATH  Google Scholar 

  • Zadorojniy A, Shwartz A (2006) Robustness of policies in constrained Markov decision processes. IEEE Trans Autom Control 51(4): 635–638

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA

    Krishnamurthy Iyer

  2. Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, Mumbai, 400 076, India

    Nandyala Hemachandra

Authors
  1. Krishnamurthy Iyer
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  2. Nandyala Hemachandra
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Correspondence to Krishnamurthy Iyer.

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Iyer, K., Hemachandra, N. Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models. Math Meth Oper Res 71, 401–425 (2010). https://doi.org/10.1007/s00186-010-0303-8

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