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

TL;DR

This paper introduces a ranking-based approach to optimize heuristic functions for planning algorithms like A*, emphasizing ranking over cost estimation, supported by theoretical analysis and experimental validation.

Contribution

It proposes a new family of ranking-based loss functions for heuristic optimization and provides theoretical insights into why focusing on cost-to-goal is challenging.

Findings

Ranking-based heuristics outperform cost-to-goal optimization in experiments

Theoretical analysis clarifies conditions for optimal heuristic efficiency

Empirical results validate the effectiveness of the proposed approach

Abstract

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.