Error Analysis and Correction for Weighted A*'s Suboptimality (Extended Version)

TL;DR

This paper investigates the inaccuracies of the suboptimality bound in Weighted A* search, providing empirical evidence, analytical insights, and a correction method to improve solution quality estimates.

Contribution

It offers the first large-scale empirical analysis of W's suboptimality bound and introduces a practical correction method to reduce its inaccuracies.

Findings

W often significantly overestimates actual suboptimality

Analytical identification of sources of error in W's bound

Correction methods can substantially improve suboptimality estimates

Abstract

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the correction frequently eliminates much of the error.