The BAO* algorithm for stochastic shortest path problems with dynamic learning

Suppose a spatial arrangement of possible obstacles needs to be traversed as swiftly as possible, and the status of the obstacles may be disambiguated en route at a cost. The goal is to find a protocol that decides what and where to disambiguate en route so as to minimize the expected length of the traversal. We call this problem the stochastic shortest path problem with dynamic learning (SDL), which has been shown to be intractable in many broad settings. In this manuscript, we establish a framework for SDL in both continuous and discrete settings and cast the problem as a Markov decision process. The state space, however, is too large to efficiently utilize the stochastic dynamic programming paradigm. We introduce an algorithm for a discretized version of the continuous setting, called the BAO* Algorithm, which is a new improvement on the AO* search algorithm that employs stronger pruning techniques, including utilization of upper bounds on path lengths (in addition to lower bounds as in AO*), and uses significantly less computational resources. The BAO* Algorithm is not polynomial-time, but it can dramatically shorten the execution time needed to find an exact solution to moderately-sized instances of the problem.