Considering a graph with unknown weights, can we find the shortest path for a
pair of nodes if we know the minimal Steiner trees associated with some subset
of nodes? That is, with respect to a fixed latent decision-making system (e.g.,
a weighted graph), we seek to solve one optimization problem (e.g., the
shortest path problem) by leveraging information associated with another
optimization problem (e.g., the minimal Steiner tree problem). In this paper,
we study such a prototype problem called \textit{query-decision regression with
task shifts}, focusing on the shortest path problem and the minimum Steiner
tree problem. We provide theoretical insights regarding the design of
realizable hypothesis spaces for building scoring models, and present two
principled learning frameworks. Our experimental studies show that such
problems can be solved to a decent extent with statistical significance.

对于一个具有未知权重的图，如果我们知道一些节点子集关联的最小 Steiner 树，那么我们能否找到一对节点的最短路径？本文研究了这样一个原型问题，称为具有任务转换的查询 - 决策回归，重点关注最短路径问题和最小 Steiner 树问题。我们提供了关于构建评分模型的可实现假设空间设计的理论洞察，并提出了两个有原则的学习框架。我们的实验研究显示，这样的问题可以在统计显著性的程度上得到较好的解决。