Variational Optimization for the Submodular Maximum Coverage Problem

TL;DR

This paper introduces a novel variational approximation method for the submodular maximum coverage problem, enabling efficient solutions with theoretical guarantees and empirical validation on various datasets.

Contribution

It presents the first variational approach based on Nemhauser divergence for SMCP, with an alternating optimization algorithm and theoretical performance analysis.

Findings

The method achieves competitive results on benchmark datasets.

The algorithm provides a curvature-dependent approximation factor.

Empirical evaluations demonstrate effectiveness across multiple applications.

Abstract

We examine the \emph{submodular maximum coverage problem} (SMCP), which is related to a wide range of applications. We provide the first variational approximation for this problem based on the Nemhauser divergence, and show that it can be solved efficiently using variational optimization. The algorithm alternates between two steps: (1) an E step that estimates a variational parameter to maximize a parameterized \emph{modular} lower bound; and (2) an M step that updates the solution by solving the local approximate problem. We provide theoretical analysis on the performance of the proposed approach and its curvature-dependent approximate factor, and empirically evaluate it on a number of public data sets and several application tasks.