Nonmonotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:18331842, 2019.
Abstract
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 largescale 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 polynomiallymany 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 constantfactor approximation algorithm for maximizing a nonmonotone 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 realworld applications to compare our algorithm with several benchmarks for nonmonotone submodular maximization. The results demonstrate that our algorithm finds competitive solutions using significantly fewer rounds and queries.
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