On Learning Linear Ranking Functions for Beam Search

Abstract

Beam search is used to maintain tractability in large search spaces at the expense of completeness and optimality. 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 while gaining computational efficiency. 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. Next, we analyze the convergence of recently proposed and modified online learning algorithms. We first provide a counter-example to an existing convergence result and then introduce alternative notions of "margin" that do imply convergence. Finally, we study convergence properties for ambiguous training data.