Lexicographic refinements in possibilistic decision trees and finite-horizon Markov decision processes

Nahla Ben Amor, Zeineb El Khalfi, Helene Fargier, Regis Sabbadin

Abstract: Possibilistic decision theory has been proposed twenty years ago and has had several extensions since then. Even though appealing for its ability to handle qualitative decision problems, possibilistic decision theory suffers from an important drawback. Qualitative possibilistic utility criteria compare acts through min and max operators, which leads to a drowning effect. To overcome this lack of decision power of the theory, several refinements have been proposed. Lexicographic refinements are particularly appealing since they allow to benefit from the Expected Utility background, while remaining qualitative. This article aims at extending lexicographic refinements to sequential decision problems i.e., to possibilistic decision trees and possibilistic Markov decision processes, when the horizon is finite. We present two criteria that refine qualitative possibilistic utilities and provide dynamic programming algorithms for calculating lexicographically optimal policies.