Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an algorithm is governed by its adaptivity, which measures the number of sequential rounds needed if the algorithm can execute polynomially-many independent oracle queries in parallel. While low adaptivity is ideal, it is not sufficient for an algorithm to be efficient in practice -- there are many applications of distributed submodular optimization where the number of function evaluations becomes prohibitively expensive. Motivated by these applications, we study the adaptivity and query complexity of submodular maximization. In this paper, we give the first constant-factor approximation algorithm for maximizing a non-monotone submodular function subject to a cardinality constraint $k$ that runs in $O(\log(n))$ adaptive rounds and makes $O(n \log(k))$ oracle queries in expectation. In our empirical study, we use three real-world applications to compare our algorithm with several benchmarks for non-monotone submodular maximization. The results demonstrate that our algorithm finds competitive solutions using significantly fewer rounds and queries.

翻译：子模最大化是一类通用优化问题，在机器学习领域（如主动学习、聚类和特征选择）具有广泛的应用。在大规模优化场景中，算法的并行运行时间由其适应性决定——该指标衡量算法在每轮并行执行多项式数量独立预言查询时所需的顺序轮次。虽然低适应性是理想特性，但这不足以确保算法在实际应用中的高效性：在分布式子模优化的诸多场景中，函数评估次数可能变得异常庞大。受此类应用启发，本文研究了子模最大化的适应性与查询复杂度。我们首次提出一种常因子近似算法，用于最大化基数约束$k$下的非单调子模函数，该算法仅需$O(\log(n))$轮自适应迭代，且期望的预言查询次数为$O(n \log(k))$。实证研究中，我们通过三个真实应用场景，将所提算法与多种非单调子模最大化基准方法进行比较。结果表明，我们的算法能以显著更少的轮次和查询次数获得具有竞争力的解。