Error analysis and correction for weighted A∗'s suboptimality

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 sub-optimality 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.