Empirical Comparison of Probabilistic and Possibilistic Markov Decision Processes Algorithms

Classical stochastic Markov Decision Processes (MDPs) and possibilistic MDPs ( -MDPs) aim at solving the same kind of problems, involving sequential decision making under uncertainty. The underlying uncertainty model (probabilistic / possibilistic) and preference model (reward / satisfaction degree) change, but the algorithms, based on dynamic programming, are similar. So, a question maybe raised about when to prefer one model to another, and for which reasons. The answer may seem obvious when the uncertainty is of an objective nature (symmetry of the problem, frequentist information) and when the problem is faced repetitively and rewards accumulate. It is less clear when uncertainty and preferences are qualitative, purely subjective and when the problem is faced only once. In this paper we carry out an empirical comparison of both types of algorithms (stochastic and possibilistic), in terms of \quality" of the solutions, and time needed to compute them.