Pathfinding is a challenging problem which generally asks to find a sequence of valid moves for an agent provided with a representation of the environment, i.e. a map, in which it operates. In this work, we consider pathfinding on binary grids and on image representations of the digital elevation models. In the former case, the transition costs are known, while in latter scenario, they are not. A widespread method to solve the first problem is to utilize a search algorithm that systematically explores the search space to obtain a solution. Ideally, the search should also be complemented with an informative heuristic to focus on the goal and prune the unpromising regions of the search space, thus decreasing the number of search iterations. Unfortunately, the widespread heuristic functions for grid-based pathfinding, such as Manhattan distance or Chebyshev distance, do not take the obstacles into account and in obstacle-rich environments demonstrate inefficient performance. As for pathfinding with image inputs, the heuristic search cannot be applied straightforwardly as the transition costs, i.e. the costs of moving from one pixel to the other, are not known. To tackle both challenges, we suggest utilizing modern deep neural networks to infer the instance-dependent heuristic functions at the pre-processing step and further use them for pathfinding with standard heuristic search algorithms. The principal heuristic function that we suggest learning is the path probability, which indicates how likely the grid cell (pixel) is lying on the shortest path (for binary grids with known transition costs, we also suggest another variant of the heuristic function that can speed up the search). Learning is performed in a supervised fashion (while we have also explored the possibilities of end-to-end learning that includes a planner in the learning pipeline). At the test time, path probability is used as the secondary heuristic for the Focal Search, a specific heuristic search algorithm that provides the theoretical guarantees on the cost bound of the resultant solution. Empirically, we show that the suggested approach significantly outperforms state-of-the-art competitors in a variety of different tasks (including out-of-the distribution instances).

中文翻译：

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用于基于格网和基于图像的寻路的生成模型


寻路是一个具有挑战性的问题，它通常要求为代理找到一系列有效的移动，该代理提供了环境的表示，即它在其中运行的地图。在这项工作中，我们考虑了二进制网格和数字高程模型的图像表示的寻路。在前一种情况下，过渡成本是已知的，而在后一种情况下，过渡成本是未知的。解决第一个问题的一种广泛方法是利用搜索算法，该系统系统地探索搜索空间以获得解决方案。理想情况下，搜索还应辅以信息丰富的启发式方法，以专注于目标并修剪搜索空间中没有希望的区域，从而减少搜索迭代的次数。遗憾的是，基于网格的寻路的广泛启发式函数（例如曼哈顿距离或切比雪夫距离）并未考虑障碍物，并且在障碍物丰富的环境中表现出低效的性能。至于使用图像输入进行寻路，启发式搜索不能直接应用，因为转换成本（即从一个像素移动到另一个像素的成本）是未知的。为了应对这两个挑战，我们建议利用现代深度神经网络在预处理步骤中推断依赖于实例的启发式函数，并进一步将它们用于标准启发式搜索算法的寻路。我们建议学习的主要启发式函数是路径概率，它表示网格单元（像素）位于最短路径上的可能性（对于具有已知转换成本的二进制网格，我们还建议使用另一种可以加快搜索速度的启发式函数变体）。 学习以监督的方式进行（同时我们还探索了端到端学习的可能性，其中包括学习管道中的规划器）。在测试时，路径概率用作焦点搜索的辅助启发式搜索，焦点搜索是一种特定的启发式搜索算法，为结果解的开销边界提供理论保证。从经验上讲，我们表明，所建议的方法在各种不同的任务（包括分布式实例外）中明显优于最先进的竞争对手。