In imitation learning for planning, parameters of heuristic functions are
optimized against a set of solved problem instances. This work revisits the
necessary and sufficient conditions of strictly optimally efficient heuristics
for forward search algorithms, mainly A* and greedy best-first search, which
expand only states on the returned optimal path. It then proposes a family of
loss functions based on ranking tailored for a given variant of the forward
search algorithm. Furthermore, from a learning theory point of view, it
discusses why optimizing cost-to-goal \hstar\ is unnecessarily difficult. The
experimental comparison on a diverse set of problems unequivocally supports the
derived theory.

本论文重新审视了启发式函数在规划中的模仿学习中的必要和充分条件，并针对给定的前向搜索算法的变体提出了一族基于排名的损失函数。另外，从学习理论的角度讨论了为什么优化成本 - 目标 h * 是不必要困难的。实验比较在多样化的问题集上明确地支持了得出的理论。

优化规划启发式算法，以排序而非估算目标开销

Optimize Planning Heuristics to Rank, not to Estimate Cost-to-Goal

While learning a heuristic function for forward search algorithms with modern
machine learning techniques has been gaining interest in recent years, there
has been little theoretical understanding of \emph{what} they should learn,
\emph{how} to train them, and \emph{why} we do so. This lack of understanding
leads to various literature performing an ad-hoc selection of datasets
(suboptimal vs optimal costs or admissible vs inadmissible heuristics) and
optimization metrics (e.g., squared vs absolute errors). Moreover, due to the
lack of admissibility of the resulting trained heuristics, little focus has
been put on the role of admissibility \emph{during} learning. This paper
articulates the role of admissible heuristics in supervised heuristic learning
using them as parameters of Truncated Gaussian distributions, which tightens
the hypothesis space compared to ordinary Gaussian distributions. We argue that
this mathematical model faithfully follows the principle of maximum entropy and
empirically show that, as a result, it yields more accurate heuristics and
converges faster during training.

通过将可接受启发式学习的参数作为截断高斯分布的参数，这篇论文阐述了可接受启发式在监督式启发式学习中的作用，证明这种数学模型忠实地遵循最大熵原理，并通过实证表明，其结果是产生更准确的启发式并在训练过程中更快地收敛。