Maximizing a Submodular Function with Bounded Curvature under an Unknown Knapsack Constraint
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This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness factor of a policy is the worst case ratio of the solution obtained by following the policy and an optimal solution that knows the knapsack capacity. We develop an algorithm with a robustness factor that is decreasing in the curvature B of the submodular function. For the extreme cases c=0 corresponding to a modular objective, it matches a previously known and best possible robustness factor of 1/2. For the other extreme case of c=1 it yields a robustness factor of ≈ 0.35 improving over the best previously known robustness factor of ≈ 0.06.
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