Submodular Maximization via Taylor Series Approximation

We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called continuous greedy algorithm attains a ratio arbitrarily close to (1 − 1/e) ≈ 0.63 using a deterministic estimation via Taylor series approximation. This drastically reduces execution time over prior art that uses sampling.

Recommended citation: Özcan, Gözde, Armin Moharrer, and Stratis Ioannidis. (2021). "Submodular Maximization via Taylor Series Approximation." Proceedings of the 2021 SIAM International Conference on Data Mining (SDM). Society for Industrial and Applied Mathematics, 2021.
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