Oversubscription planning (OSP) is the problem of choosing an action sequence which reaches a state with a high utility, given a budget for total action cost. This formulation allows us to handle situations with under-constrained resources, which do not allow us to achieve all possible goal facts. In optimal OSP, the task is further constrained to finding a path which achieves a state with maximal utility. An incremental BFBB search algorithm with landmark-based approximations, proposed for OSP heuristic search to address tasks with non-negative and 0-binary utility functions. Incremental BFBB maintained with the best solution so far and a set of reference states, extended with all the non-redundant value-carrying states discovered during the search. Each iteration requires search re-start in order to exploit the new knowledge obtained along the search. Recent work proposed an approach of relative estimation of achievements with value-driven landmarks to address arbitrary utility functions, which incrementally improves the best existing solution so far eliminating the need to maintain a set of reference states. We now propose a progressive frontier search algorithm, which alleviates the need to re-start from scratch once new information is acquired by capturing the frontier achieved at the end of each iteration which is used as a dynamic reference point to continue the search, leading to improved efficiency of the search.