Trajectory Constraint Heuristics for Optimal Probabilistic Planning

Search algorithms such as LAO* and LRTDP coupled with admissible heuristics are widely used methods for optimal probabilistic planning. Their effectiveness depends on the degree to which heuristics are able to approximate the optimal cost of a state. Most common domain-independent heuristics, however, rely on determinization, and ignore the probabilities associated with different effects of actions. Here, we present a method for decomposing a probabilistic planning problem into subproblems by constraining possible action outcomes. Admissible heuristics evaluated for each subproblem can then be combined via a weighted sum to obtain an admissible heuristic for the original problem that takes into account a limited amount of probabilistic information. We use this approach to derive new admissible heuristics for probabilistic planning, and show that for some problems they are significantly more informative than existing heuristics, leading to up to an order of magnitude speedups in the time to converge to an optimal policy.