Query-decision Regression between Shortest Path and Minimum Steiner Tree
This addresses a query-decision regression problem with task shifts for graph optimization, but it appears incremental as it builds on existing concepts without claiming broad breakthroughs.
The paper tackles the problem of predicting shortest paths in a graph with unknown weights by using information from minimal Steiner trees, presenting theoretical insights and learning frameworks. Experimental results show the approach can solve such problems to a decent extent with statistical significance.
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.