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Bayesian Learning of Noisy Markov Decision Processes

  • Sumeetpal S. Singh


  • Nicolas Chopin


  • Nick Whiteley


This work addresses the problem of estimating the optimal value function in a MarkovDecision Process from observed state-action pairs. We adopt a Bayesian approach toinference, which allows both the model to be estimated and predictions about actions tobe made in a unified framework, providing a principled approach to mimicry of a controlleron the basis of observed data. A new Markov chain Monte Carlo (MCMC) sampler isdevised for simulation from the posterior distribution over the optimal value function.This step includes a parameter expansion step, which is shown to be essential for goodconvergence properties of the MCMC sampler. As an illustration, the method is appliedto learning a human controller.

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2010-36.

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Length: 36
Date of creation: 2010
Date of revision:
Handle: RePEc:crs:wpaper:2010-36
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  1. Susumu Imai & Neelam Jain, 2005. "Bayesian Estimation of Dynamic Discrete Choice Models," 2005 Meeting Papers 432, Society for Economic Dynamics.
  2. repec:bla:restud:v:60:y:1993:i:3:p:497-529 is not listed on IDEAS
  3. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
  4. John F. Geweke & Michael P. Keane & David E. Runkle, 1994. "Alternative computational approaches to inference in the multinomial probit model," Staff Report 170, Federal Reserve Bank of Minneapolis.
  5. Wolpin, Kenneth I, 1984. "An Estimable Dynamic Stochastic Model of Fertility and Child Mortality," Journal of Political Economy, University of Chicago Press, vol. 92(5), pages 852-74, October.
  6. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
  7. V. Joseph Hotz & Robert A. Miller, 1992. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Working Papers 9202, Harris School of Public Policy Studies, University of Chicago.
  8. Gotz, Glenn A. & McCall, John J., 1980. "Estimation in sequential decisionmaking models : A methodological note," Economics Letters, Elsevier, vol. 6(2), pages 131-136.
  9. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
  10. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
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