Regularized nonmonotone submodular maximization

In this paper, we present a thorough study of the regularized submodular maximization problem, in which the objective $ f:=g-\ell $ f := g − ℓ can be expressed as the difference between a submodular function and a modular function. This problem has drawn much attention in recent years. While existin...

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Bibliographic Details
Published in:Optimization Vol. 73; no. 6; pp. 1739 - 1765
Main Authors: Lu, Cheng, Yang, Wenguo, Gao, Suixiang
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.06.2024
Taylor & Francis LLC
Subjects:
Algorithms
Constraints
continuous greedy algorithm
Greedy algorithms
Maximization
Optimization
random greedy algorithm
regularized problem
sampling
Submodular maximization
Weighting
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this paper, we present a thorough study of the regularized submodular maximization problem, in which the objective $ f:=g-\ell $ f := g − ℓ can be expressed as the difference between a submodular function and a modular function. This problem has drawn much attention in recent years. While existing works focuses on the case of g being monotone, we investigate the problem with a nonmonotone g. The main technique we use is to introduce a distorted objective function, which varies weights of the submodular component g and the modular component ℓ during the iterations of the algorithm. By combining the weighting technique and measured continuous greedy algorithm, we present an algorithm for the matroid-constrained problem, which has a provable approximation guarantee. In the cardinality-constrained case, we utilize random greedy algorithm and sampling technique together with the weighting technique to design two efficient algorithms. Moreover, we consider the unconstrained problem and propose a much simpler and faster algorithm compared with the algorithms for solving the problem with a cardinality constraint.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2023.2173968