Representations of Decision-Theoretic Planning Tasks
Goal-directed Markov Decision Process models (GDMDPs) are good models for many decision-theoretic planning tasks. They have been used in conjunction with two different reward structures, namely the goal-reward representation and the action-penalty representation. We apply GDMDPs to planning tasks in the presence of traps such as steep slopes for outdoor robots or staircases for indoor robots, and study the differences between the two reward structures. In these situations, achieving the goal is often the primary objective while minimizing the travel time is only of secondary importance. We show that the action-penalty representation without discounting guarantees that the optimal plan achieves the goal for sure (if this is possible) but neither the action-penalty representation with discounting nor the goal-reward representation with discounting have this property. We then show exactly when this trapping phenomenon occurs, using a novel interpretation for discounting, namely that it models agents that use convex exponential utility functions and thus are optimistic in the face of uncertainty. Finally, we show how the trapping phenomenon can be eliminated with our Selective State-Deletion Method.