Symbolic Heuristic Search Using Decision Diagrams

Abstract

We show how to use symbolic model-checking techniques in heuristic search algorithms for both deterministic and decision-theoretic planning problems. A symbolic approach exploits state abstraction by using decision diagrams to compactly represent sets of states and operators on sets of states. In earlier work, symbolic model-checking techniques have been used to find plans that minimize the number of steps needed to reach a goal. Our approach generalizes this by showing how to find plans that minimize the expected cost of reaching a goal. For this generalization, we use algebraic decision diagrams instead of binary decision diagrams. In particular, we show that algebraic decision diagrams provide a compact representation of state evaluation functions. We describe symbolic generalizations of A* search for deterministic planning and of LAO* search for decision-theoretic planning problems formalized as Markov decision processes. We report experimental results and discuss issues for future work.