Parallel algorithm for non-monotone DR-submodular maximization

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Date
2020-08-14
DOI
Authors
Ene, Alina
Nguyen, Huy Le
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Published version
OA Version
Citation
Alina Ene, Huy Le Nguyen. 2020. "Parallel Algorithm for Non-Monotone DR-Submodular Maximization." International Conference on Machine Learning
Abstract
In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy 𝜖, our algorithm achieves a 1/e − 𝜖 approximation using O(log n log(1/𝜖 )/𝜖^3) parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant 𝜖. Previous algorithms achieve worse approximation guarantees using Ω (log^2 n) parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.
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Copyright 2020 by the author(s).