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Unifying Nondeterministic and Probabilistic Planning Through Imprecise Markov Decision Processes

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Advances in Artificial Intelligence - IBERAMIA-SBIA 2006 (IBERAMIA 2006, SBIA 2006)

Abstract

This paper proposes an unifying formulation for nondeterministic and probabilistic planning. These two strands of AI planning have followed different strategies: while nondeterministic planning usually looks for minimax (or worst-case) policies, probabilistic planning attempts to maximize expected reward. In this paper we show that both problems are special cases of a more general approach, and we demonstrate that the resulting structures are Markov Decision Processes with Imprecise Probabilities (MDPIPs). We also show how existing algorithms for MDPIPs can be adapted to planning under uncertainty.

Project funded by Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP) process number 04/09568-0.

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References

  1. Ghallab, M., Nau, D., Traverso, P.: Automated Planning: Theory & Practice. Morgan Kaufmann, San Francisco (2004)

    MATH  Google Scholar 

  2. Bonet, B., Geffner, H.: Learning Depth-First Search: A unified approach to heuristic search in deterministic and non-deterministic settings, and its application to MDPs. In: ICAPS (2006) (to appear)

    Google Scholar 

  3. Bonet, B., Geffner, H.: Labeled RTDP: Improving the convergence of real-time dynamic programming. In: ICAPS, Trento, Italy, pp. 12–21. AAAI Press, Menlo Park (2003)

    Google Scholar 

  4. Guestrin, C., Koller, D., Parr, R., Venkataraman, S.: Efficient solution algorithms for factored MDPs. J. Artif. Intell. Res (JAIR) 19, 399–468 (2003)

    MATH  MathSciNet  Google Scholar 

  5. Bertoli, P., Cimatti, A., Roveri, M., Traverso, P.: Planning in nondeterministic domains under partial observability via symbolic model checking. In: IJCAI, pp. 473–478 (2001)

    Google Scholar 

  6. Bonet, B., Geffner, H.: Planning with incomplete information as heuristic search in belief space. In: ICAPS, Breckenridge, CO, pp. 52–61. AAAI Press, Menlo Park (2000)

    Google Scholar 

  7. Luce, D., Raiffa, H.: Games and Decisions. Dover edn., Mineola (1957)

    Google Scholar 

  8. Berger, J.O.: Statistical Decision Theory and Bayesian Analysis. Springer, Heidelberg (1985)

    MATH  Google Scholar 

  9. Knight, F.H.: Risk, Uncertainty, and Profit. Hart, Schaffner & Marx. Houghton Mifflin Company, Boston (1921)

    Google Scholar 

  10. Levi, I.: The Enterprise of Knowledge. MIT Press, Cambridge (1980)

    Google Scholar 

  11. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)

    MATH  Google Scholar 

  12. Walley, P.: Measures of uncertainty in expert systems. AI 83, 1–58 (1996)

    MathSciNet  Google Scholar 

  13. Seidenfeld, T., Kadane, J.B., Schervish, M.J.: On the shared preferences of two Bayesian decision makers. The Journal of Philosophy 86(5), 225–244 (1989)

    Article  MathSciNet  Google Scholar 

  14. Seidenfeld, T., Schervish, M.: Two perspectives on consensus for (Bayesian) inference and decisions. IEEE Transactions on Systems, Man and Cybernetics 20(1), 318–325 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  15. Huber, P.J.: Robust Statistics. Wiley, New York (1980)

    Google Scholar 

  16. Kadane, J.B. (ed.): Robustness of Bayesian Analyses. Studies in Bayesian econometrics, vol. 4. Elsevier Science Pub. Co., New York (1984)

    MATH  Google Scholar 

  17. Frisch, A.M., Haddawy, P.: Anytime deduction for probabilistic logic. Artificial Intelligence 69, 93–122 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  18. Halpern, J.Y.: Reasoning about uncertainty. MIT Press, Cambridge (2003)

    MATH  Google Scholar 

  19. Nilsson, N.J.: Probabilistic logic. Artificial Intelligence 28, 71–87 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  20. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  21. Anrig, B., Bissig, R., Haenni, R., Kohlas, J., Lehmann, N.: Probabilistic argumentation systems: Introduction to assumption-based modeling with ABEL. Technical Report 99-1, Institute of Informatics, University of Fribourg (1999)

    Google Scholar 

  22. Cozman, F.G.: Credal networks. AI 120, 199–233 (2000)

    MATH  MathSciNet  Google Scholar 

  23. Cozman, F.G.: Graphical models for imprecise probabilities. International Journal of Approximate Reasoning 39(2-3), 167–184 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  24. Fagiuoli, E., Zaffalon, M.: 2U: An exact interval propagation algorithm for polytrees with binary variables. Artificial Intelligence 106(1), 77–107 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  25. de Cooman, G., Cozman, F., Moral, S., Walley, P. (eds.): Proceedings of the First International Symposium on Imprecise Probabilities and Their Applications (SIPTA), Universiteit Gent, Ghent, Belgium (1999)

    Google Scholar 

  26. de Cooman, G., Fine, T.L., Seidenfeld, T.: Proceedings of the 2nd International SIPTA. Shaker Publishing, The Netherlands (2001)

    Google Scholar 

  27. Bernard, J.M., Seidenfeld, T., Zaffalon, M. (eds.): Proceedings of the 3rd International SIPTA Carleton Scientific, Lugano, Switzerland (2003)

    Google Scholar 

  28. Cozman, F.G., Nau, R., Seidenfeld, T.: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications. SIPTA (2005)

    Google Scholar 

  29. White III, C.C., Eldeib, H.K.: Markov decision processes with imprecise transition probabilities. Operations Research 42(4), 739–749 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  30. Satia, J.K., Lave Jr., R.E.: Markovian decision processes with uncertain transition probabilities. Operations Research 21(3), 728–740 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  31. Howard, R.A.: Dynamic Porgramming and Markov Processes. MIT Press, Cambridge (1960)

    Google Scholar 

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Trevizan, F.W., Cozman, F.G., de Barros, L.N. (2006). Unifying Nondeterministic and Probabilistic Planning Through Imprecise Markov Decision Processes. In: Sichman, J.S., Coelho, H., Rezende, S.O. (eds) Advances in Artificial Intelligence - IBERAMIA-SBIA 2006. IBERAMIA SBIA 2006 2006. Lecture Notes in Computer Science(), vol 4140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874850_54

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  • DOI: https://doi.org/10.1007/11874850_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45462-5

  • Online ISBN: 978-3-540-45464-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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