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.

我们提出了一种新的算法，可以在实践中有效地解决非单调受限子模型最大化问题，结合了 0.385 的逼近保证和低的查询复杂度。通过在各种机器学习应用中进行实验，包括电影推荐、图像摘要等，我们评估了我们算法的实验性能，证明了我们方法的功效。