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Title: Parallel Algorithm for Non-Monotone DR-Submodular Maximization
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 epsilon, our algorithm achieves a 1/e−epsilon approximation using O(logn*log(1/epsilon)/epsilon^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 epsilon. 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.  more » « less
Award ID(s):
1750716
NSF-PAR ID:
10212628
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Proceedings of Machine Learning Research
Volume:
119
ISSN:
2640-3498
Page Range / eLocation ID:
2902-2911
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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