Recent machine-learning approaches to deterministic search and domain-independent planning employ policy learning to speed up search. Unfortunately, when attempting to solve a search problem by successively applying a policy, no guarantees can be given on solution quality. The problem of how to effectively use a learned policy within a bounded-suboptimal search algorithm remains largely as an open question. In this paper, we propose various ways in which such policies can be integrated into

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... l Search, assuming that the policy is a neural network classifier. Furthermore, we provide mathematical foundations for some of the resulting algorithms. To evaluate the resulting algorithms over a number of policies with varying accuracy, we use synthetic policies which can be generated for a target accuracy for problems where the search space can be held in memory. We evaluate our focal search variants over three benchmark domains using our synthetic approach, and on the 15-puzzle using a neural network learned using 1.5 million examples. We observe that Discrepancy Focal Search, which we show expands the node which maximizes an approximation of the probability that its corresponding path is a prefix of an optimal path, obtains, in general, the best results in terms of runtime and solution quality.