The interaction of representations and planning objectives for decision-theoretic planning tasks
This article studies decision-theoretic planning or reinforcement learning in the presence of traps such as steep slopes for outdoor robots or staircases for indoor robots. In this case, achieving the goal from the start is often the primary objective while minimizing the travel time is only of secondary importance. This article studies how this planning objective interacts with possible representations of the planning tasks, namely whether to use a discount factor that is one or smaller than one and whether to use the action-penalty or the goal-reward representation. It is shown that the action-penalty representation without discounting guarantees that the plan that maximizes the expected reward also achieves the goal from the start (provided that this is possible) but neither the action-penalty representation with discounting nor the goal-reward representation with discounting have this property. The article then shows exactly when this trapping phenomenon occurs, using a novel interpretation of discounting, namely that it models agents that use convex exponential utility functions and thus are optimistic in the face of uncertainty. Finally, it is shown how the selective state-deletion method can be used in conjunction with standard decision-theoretic planners to eliminate the trapping phenomenon.