Lexicographic refinements in stationary possibilistic Markov Decision Processes

• Published in: International journal of approximate reasoning Vol. 103; no. Virtual special issue on the 14th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017); pp. 343 - 363
• Main Authors: Ben Amor, Nahla, El Khalfi, Zeineb, Fargier, Hélène, Sabbadin, Régis
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2018; Elsevier
• Subjects: Computer Science; Data Structures and Algorithms; Lexicographic comparisons; Machine Learning; Markov Decision Process; Possibilistic qualitative utilities; Possibility theory; Possibility theory; Markov Decision Process; Lexicographic comparisons; Possibilistic qualitative utilities; Markov decision process
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2018.10.011

Possibilistic Markov Decision Processes offer a compact and tractable way to represent and solve problems of sequential decision under qualitative uncertainty. Even though appealing for its ability to handle qualitative problems, this model suffers from the drowning effect that is inherent to possibilistic decision theory. The present1 paper proposes to escape the drowning effect by extending to stationary possibilistic MDPs the lexicographic preference relations defined by Fargier and Sabbadin [13] for non-sequential decision problems. We propose a value iteration algorithm and a policy iteration algorithm to compute policies that are optimal for these new criteria. The practical feasibility of these algorithms is then experimented on different samples of possibilistic MDPs.