Time is a crucial variable in planning and often requires special attention since it introduces a specific structure along with additional complexity, especially in the case of decision under uncertainty. In this paper, after reviewing and comparing MDP frameworks designed to deal with temporal problems, we focus on Generalized Semi-Markov Decision Processes (GSMDP) with observable time. We highlight the inherent structure and complexity of these problems and present the differences with classical reinforcement learning problems. Finally, we introduce a new simulation-based reinforcement learning method for solving GSMDP, bringing together results from simulation-based policy iteration, regression techniques and simulation theory. We illustrate our approach on a subway network control example.
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