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We consider a class of submodular maximization problems in whichdecision-makers have limited access to the objective function. We explorescenarios where the decision-maker can observe only pairwise information, i.e.,can evaluate the objective function on sets of size two. We begin with anegative result that no algorithm using only $k$-wise information can guaranteeperformance better than $k/n$. We present two algorithms that utilize onlypairwise information about the function and characterize their performancerelative to the optimal, which depends on the curvature of the submodularfunction. Additionally, if the submodular function possess a property calledsupermodularity of conditioning, then we can provide a method to bound theperformance based purely on pairwise information. The proposed algorithms offersignificant computational speedups over a traditional greedy strategy. Aby-product of our study is the introduction of two new notions of curvature,the $k$-Marginal Curvature and the $k$-Cardinality Curvature. Finally, wepresent experiments highlighting the performance of our proposed algorithms interms of approximation and time complexity.

Submodular Maximization with Limited Function Access