Bayesian A* Tree Search with Expected O(N) Convergence Rates for Road Tracking

This paper develops a theory for the convergence rates of A* algorithms for real-world vision problems, such as road tracking, which can be formulated in terms of maximizing a reward function derived using Bayesian probability theory. Such problems are well suited to A* tree search and it can be shown that many algorithms proposed to solve them are special cases, or variants, of A*. Moreover, the Bayesian formulation naturally defines a probability distribution on the ensemble of problem instances, which we call the Bayesian Ensemble. We analyze the Bayesian ensemble, using techniques from information theory, and mathematically prove expected O(N) convergence rates of inadmissible A* algorithms. These rates depend on an “order parameter” which characterizes the difficulty of the problem.