Is diff a* search admissible?
OAHC2022 opened this issue · comments
Hi,
I am very interested in your work and want to get a good understanding of this code. However, I have a question about how heuristic is implemented here.
I am looking at this line of code in differentiable_astar.py. From my understanding, the heuristic function produces a h value to be greater than 1 while the costmap values are between 0 and 1. If the g_ratio value is set as default (0.5), wouldn't this heuristic value violate the admissible assumption for a*? Yet, when I ran the example code you provided here, the model seemed to be able to train successfully and produce good result. I am not sure why this works. Maybe I am missing something? Could you please help me with this?
Thanks!
Hi @OAHC2022 , thanks for the question.
That is a good point. As you properly recognized, Neural A* does not satisfy admissibility and as a result, it’s not an optimal solver.
Empirically, Neural A* learns to give costs lower than 1.0 to nodes when the nodes seem to be a part of the shortest paths. So these nodes are more likely to be selected than other nodes, despite the heuristic function is not admissible.
FYI a follow-up work from another group tried to design an admissible version https://arxiv.org/pdf/2105.01480.pdf, which however does not work well yet. I think extending Neural A* to be an optimal solver is an interesting future direction.
Oh thank you very much! This makes sense :)