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Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Author(s):
Shirota Filho, Ricardo ; Cozman, Fabio Gagliardi ; Trevizan, Felipe Werndl ; de Campos, Cassio Polpo ; de Barros, Leliane Nunes ; DeCooman, G ; Vejnarova, J ; Zaffalon, M
Total Authors: 8
Document type: Journal article
Source: ISIPTA 07-PROCEEDINGS OF THE FIFTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY:THEORIES AND APPLICATIONS; v. N/A, p. 3-pg., 2007-01-01.
Abstract

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Gamma-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to "factored" models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (N4DPSTs), that unifies the fields of probabilistic and "nondeterministic" planning in artificial intelligence research. (AU)