  Lazy graph search algorithms are efficient at solving motion planning
problems where edge evaluation is the computational bottleneck. These
algorithms work by lazily computing the shortest potentially feasible path,
evaluating edges along that path, and repeating until a feasible path is found.
The order in which edges are selected is critical to minimizing the total
number of edge evaluations: a good edge selector chooses edges that are not
only likely to be invalid, but also eliminates future paths from consideration.
We wish to learn such a selector by leveraging prior experience. We formulate
this problem as a Markov Decision Process (MDP) on the state of the search
problem. While solving this large MDP is generally intractable, we show that we
can compute oracular selectors that can solve the MDP during training. With
access to such oracles, we use imitation learning to find effective policies.
If new search problems are sufficiently similar to problems solved during
training, the learned policy will choose a good edge evaluation ordering and
solve the motion planning problem quickly. We evaluate our algorithms on a wide
range of 2D and 7D problems and show that the learned selector outperforms
baseline commonly used heuristics. We further provide a novel theoretical
analysis of lazy search in a Bayesian framework as well as regret guarantees on
our imitation learning based approach to motion planning.
