Practical $0.385$-Approximation for Submodular Maximization Subject to a Cardinality Constraint

TL;DR

This paper introduces a new practical algorithm for non-monotone submodular maximization under a cardinality constraint that achieves a 0.385-approximation with low computational complexity, outperforming previous practical methods.

Contribution

The authors propose a novel algorithm that balances approximation quality and efficiency, achieving a 0.385-approximation with low query complexity, improving practical applicability.

Findings

The algorithm achieves a 0.385-approximation guarantee.

Experimental results demonstrate effectiveness in real-world applications.

The method outperforms existing practical algorithms in efficiency and quality.

Abstract

Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The current state-of-the-art is a recent $0.401$-approximation algorithm, but its computational complexity makes it highly impractical. The best practical algorithms for the problem only guarantee $1/e$-approximation. In this work, we present a novel algorithm for submodular maximization subject to a cardinality constraint that combines a guarantee of $0.385$-approximation with a low and practical query complexity of $O(n+k^2)$. Furthermore, we evaluate the empirical performance of our algorithm in experiments based on various machine learning applications, including Movie Recommendation, Image Summarization, and more. These experiments demonstrate the efficacy of our approach.