Coarse-to-fine dynamic programming

We introduce an extension of dynamic programming, we call "coarse-to-fine dynamic programming" (CFDP), ideally suited to DP problems with large state space. CFDP uses dynamic programming to solve a sequence of coarse approximations which are lower bounds to the original DP problem. These approximations are developed by merging states in the original graph into "superstates" in a coarser graph which uses an optimistic arc cost between superstates. The approximations are designed so that CFDP terminates when the optimal path through the original state graph has been found. CFDP leads to significant decreases in the amount of computation necessary to solve many DP problems and can, in some instances, make otherwise infeasible computations possible. CFDP generalizes to DP problems with continuous state space and we offer a convergence result for this extension. We demonstrate applications of this technique to optimization of functions and boundary estimation in mine recognition