Submodular Cost Submodular Cover with an Approximate Oracle

In this work, we study the Submodular Cost Submodular Cover problem, which is to minimize the submodular cost required to ensure that the submodular benefit function exceeds a given threshold. Existing approximation ratios for the greedy algorithm assume a value oracle to the benefit function. However, access to a value oracle is not a realistic assumption for many applications of this problem, where the benefit function is difficult to compute. We present two incomparable approximation ratios for this problem with an approximate value oracle and demonstrate that the ratios take on empirically relevant values through a case study with the Influence Threshold problem in online social networks.