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Efficiently solving problems with large action spaces using A* search hasbeen of importance to the artificial intelligence community for decades. Thisis because the computation and memory requirements of A* search grow linearlywith the size of the action space. This burden becomes even more apparent whenA* search uses a heuristic function learned by computationally expensivefunction approximators, such as deep neural networks. To address this problem,we introduce Q* search, a search algorithm that uses deep Q-networks to guidesearch in order to take advantage of the fact that the sum of the transitioncosts and heuristic values of the children of a node can be computed with asingle forward pass through a deep Q-network without explicitly generatingthose children. This significantly reduces computation time and requires onlyone node to be generated per iteration. We use Q* search to solve the Rubik'scube when formulated with a large action space that includes 1872 meta-actionsand find that this 157-fold increase in the size of the action space incursless than a 4-fold increase in computation time and less than a 3-fold increasein number of nodes generated when performing Q* search. Furthermore, Q* searchis up to 129 times faster and generates up to 1288 times fewer nodes than A*search. Finally, although obtaining admissible heuristic functions from deepneural networks is an ongoing area of research, we prove that Q* search isguaranteed to find a shortest path given a heuristic function that neitheroverestimates the cost of a shortest path nor underestimates the transitioncost.

A* Search Without Expansions: Learning Heuristic Functions with Deep Q-Networks