  We propose a new approach for solving a class of discrete decision making
problems under uncertainty with positive cost. This issue concerns multiple and
diverse fields such as engineering, economics, artificial intelligence,
cognitive science and many others. Basically, an agent has to choose a single
or series of actions from a set of options, without knowing for sure their
consequences. Schematically, two main approaches have been followed: either the
agent learns which option is the correct one to choose in a given situation by
trial and error, or the agent already has some knowledge on the possible
consequences of his decisions; this knowledge being generally expressed as a
conditional probability distribution. In the latter case, several optimal or
suboptimal methods have been proposed to exploit this uncertain knowledge in
various contexts. In this work, we propose following a different approach,
based on the geometric intuition of distance. More precisely, we define a goal
independent quasimetric structure on the state space, taking into account both
cost function and transition probability. We then compare precision and
computation time with classical approaches.
