Practical $0.385$-Approximation for Submodular Maximization Subject to a Cardinality Constraint
This work addresses the trade-off between approximation guarantees and practical efficiency in submodular maximization for machine learning applications, offering an incremental improvement over existing methods.
The paper tackles the problem of non-monotone constrained submodular maximization with a cardinality constraint, presenting an algorithm that achieves a 0.385-approximation guarantee with practical query complexity of O(n+k^2), as validated in experiments on applications like Movie Recommendation and Image Summarization.
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.