Coarse-to-Fine Dynamic Programming

We introduce an extension of dynamic programming DP 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 when CFDP terminates the optimal path through the original state graph has been found CFDP leads to signi cant 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 o er a convergence result for this extension The computation of the approximations requires that we bound the arc cost over all possible arcs associated with an adjacent pair of superstates thus the feasibility of our proposed method requires the identi cation of such a lower bound We demonstrate applications of this technique to optimization of functions and boundary estimation in mine recognition Index Terms dynamic programming A star mine recognition brachistochrone iterated com plete path coarse to ne global optimization