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.

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