Time Complexity of Iterative-Deepening A*: The Informativeness Pathology (Abstract)

Korf et al. (2001) developed a formula, KRE, to predict the number of nodes expanded by IDA* for consistent heuristics. They proved that the predictions were exact asymptotically (in the limit of large d), and experimentally showed that they were extremely accurate even at depths of practical interest. Zahavi et al. (2010) generalized KRE to work with inconsistent heuristics and to account for the heuristic values of the start states. Their formula, CDP, is intuitively described in the next section. For a full description of CDP the reader is referred to Zahavi et al. (2010). Our research advances this line of research in three ways. First, we identify a source of prediction error that has hitherto been overlooked. We call it the “discretization effect”. Second, we disprove the intuitively appealing idea that a “more informed” prediction system cannot make worse predictions than a “less informed” one. More informed systems are more susceptible to the discretization effect, and in our experiments the more informed system makes poorer predictions. Our third contribution is a method, called “ truncation”, which makes a prediction system less informed, in a carefully chosen way, so as to improve its predictions by reducing the discretization effect. In our experiments truncation improved predictions substantially.