Learning Linear Ranking Functions for Beam Search with Application to Planning

Yuehua Xu, Alan Fern, Sungwook Yoon.

Year: 2009, Volume: 10, Issue: 54, Pages: 1571−1610


Beam search is commonly used to help maintain tractability in large search spaces at the expense of completeness and optimality. Here we study supervised learning of linear ranking functions for controlling beam search. The goal is to learn ranking functions that allow for beam search to perform nearly as well as unconstrained search, and hence gain computational efficiency without seriously sacrificing optimality. In this paper, we develop theoretical aspects of this learning problem and investigate the application of this framework to learning in the context of automated planning. We first study the computational complexity of the learning problem, showing that even for exponentially large search spaces the general consistency problem is in NP. We also identify tractable and intractable subclasses of the learning problem, giving insight into the problem structure. Next, we analyze the convergence of recently proposed and modified online learning algorithms, where we introduce several notions of problem margin that imply convergence for the various algorithms. Finally, we present empirical results in automated planning, where ranking functions are learned to guide beam search in a number of benchmark planning domains. The results show that our approach is often able to outperform an existing state-of-the-art planning heuristic as well as a recent approach to learning such heuristics.