Approximation guarantees for parallelized maximization of monotone non-submodular function with a cardinality constraint

Emerging applications in machine learning have imposed the problem of monotone non-submodular maximization subject to a cardinality constraint. Meanwhile, parallelism is prevalent for large-scale optimization problems in bigdata scenario while adaptive complexity is an important measurement of paral...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 43; no. 5; pp. 1671 - 1690
Main Authors: Cui, Min, Xu, Dachuan, Guo, Longkun, Wu, Dan
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2022
Springer Nature B.V
Subjects:
Adaptive algorithms
Approximation
Combinatorics
Convex and Discrete Geometry
Machine learning
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Maximization
Operations Research/Decision Theory
Optimization
Theory of Computation
Non-submodular optimization
Submodularity ratio
Parallel algorithm
Cardinality constraint
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:Emerging applications in machine learning have imposed the problem of monotone non-submodular maximization subject to a cardinality constraint. Meanwhile, parallelism is prevalent for large-scale optimization problems in bigdata scenario while adaptive complexity is an important measurement of parallelism since it quantifies the number of sequential rounds by which the multiple independent functions can be evaluated in parallel. For a monotone non-submodular function and a cardinality constraint, this paper devises an adaptive algorithm for maximizing the function value with the cardinality constraint through employing the generic submodularity ratio γ to connect the monotone set function with submodularity. The algorithm achieves an approximation ratio of 1 - e - γ 2 - ε and consumes O ( log ( n / η ) / ε 2 ) adaptive rounds and O ( n log log ( k ) / ε 3 ) oracle queries in expectation. Furthermore, when γ = 1 , the algorithm achieves an approximation guarantee 1 - 1 / e - ε , achieving the same ratio as the state-of-art result for the submodular version of the problem.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-021-00719-z