Submodular Maximization via Taylor Series Approximation

TL;DR

This paper introduces a deterministic Taylor series-based approximation method for submodular maximization under matroid constraints, achieving near-optimal ratios with significantly reduced computation time.

Contribution

It presents a novel deterministic approach using Taylor series to improve efficiency in submodular maximization with matroid constraints.

Findings

Achieves approximation ratio close to 0.63.

Reduces execution time compared to sampling-based methods.

Applicable to functions expressed via analytic and multilinear compositions.

Abstract

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 $(1-1/e) \approx 0.63$ using a deterministic estimation via Taylor series approximation. This drastically reduces execution time over prior art that uses sampling.