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• W2949203029 abstract "We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $alpha$ and the submodularity ratio $gamma$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $frac{1}{alpha}(1- e^{-gammaalpha})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications." @default.
• W2949203029 created "2019-06-27" @default.
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• W2949203029 date "2017-03-06" @default.
• W2949203029 modified "2023-09-26" @default.
• W2949203029 title "Guarantees for Greedy Maximization of Non-submodular Functions with Applications" @default.
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