Indefinite-Horizon POMDPs with Action-Based Termination

For decision-theoretic planning problems with an indefinite horizon, plan execution terminates after a finite number of steps with probability one, but the number of steps until termination (i.e., the horizon) is uncertain and unbounded. In the traditional approach to modeling such problems, called a stochastic shortest-path problem, plan execution terminates when a particular state is reached, typically a goal state. We consider a model in which plan execution terminates when a stopping action is taken. We show that an action-based model of termination has several advantages for partially observable planning problems. It does not require a goal state to be fully observable; it does not require achievement of a goal state to be guaranteed; and it allows a proper policy to be found more easily. This framework allows many partially observable planning problems to be modeled in a more realistic way that does not require an artificial discount factor.