Short-Sighted Stochastic Shortest Path Problems

Algorithms to solve probabilistic planning problems can be classified in probabilistic planners and replanners. Probabilistic planners invest significant computational effort to generate a closed policy, i.e., a mapping function from every state to an action, and these solutions never “fail” if the problem correctly models the environment. Alternatively, replanners computes a partial policy, i.e., a mapping function from a set of the state space to an action, and when and if such policy fails during execution in the environment, the replanner is re-invoked to plan again from the failed state. In this paper, we introduce a special case of Stochastic Shortest Path Problems (SSPs), the short-sighted SSPs, in which every state has positive probability of being reached using at most t actions. We introduce the novel algorithm Short-Sighted Probabilistic Planner (SSiPP) that solves SSPs through short-sighted SSPs and guarantees that at least t actions can be executed without replanning. Therefore, by varying t, SSiPP can behave as either a probabilistic planner by computing closed policies, or a replanner by computing partial policies. Moreover, we prove that SSiPP is asymptotically optimal, making SSiPP the only planner that, at the same time, guarantees optimality and offers a bound in the minimum number of actions executed without replanning. We empirically compare SSiPP with the winners of the previous probabilistic planning competitions and, in 81.7% of the problems, SSiPP performs at least as good as the best competitor.