  The pathfinding problem, which aims to identify a collision-free path between
two points, is crucial for many applications, such as robot navigation and
autonomous driving. Classic methods, such as A$^*$ search, perform well on
small-scale maps but face difficulties scaling up. Conversely, data-driven
approaches can improve pathfinding efficiency but require extensive data
labeling and lack theoretical guarantees, making it challenging for practical
applications. To combine the strengths of the two methods, we utilize the
imperative learning (IL) strategy and propose a novel self-supervised
pathfinding framework, termed imperative learning-based A$^*$ (iA$^*$).
Specifically, iA$^*$ is a bilevel optimization process where the lower-level
optimization is dedicated to finding the optimal path by a differentiable A$^*$
search module, and the upper-level optimization narrows down the search space
to improve efficiency via setting suitable initial values from a data-driven
model. Besides, the model within the upper-level optimization is a fully
convolutional network, trained by the calculated loss in the lower-level
optimization. Thus, the framework avoids extensive data labeling and can be
applied in diverse environments. Our comprehensive experiments demonstrate that
iA$^*$ surpasses both classical and data-driven methods in pathfinding
efficiency and shows superior robustness among different tasks, validated with
public datasets and simulation environments.
