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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| Vydané v: | Optimization Ročník 73; číslo 6; s. 1739 - 1765 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. In this paper, we present a thorough study of the regularized submodular maximization problem, in which the objective 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. |
| Author | Lu, Cheng Yang, Wenguo Gao, Suixiang |
| Author_xml | – sequence: 1 givenname: Cheng surname: Lu fullname: Lu, Cheng organization: University of Chinese Academy of Sciences – sequence: 2 givenname: Wenguo surname: Yang fullname: Yang, Wenguo email: yangwg@ucas.ac.cn organization: University of Chinese Academy of Sciences – sequence: 3 givenname: Suixiang surname: Gao fullname: Gao, Suixiang organization: University of Chinese Academy of Sciences |
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| Cites_doi | 10.1007/BFb0121195 10.1145/956750.956769 10.1007/BF01588971 10.1287/moor.2016.0842 10.1006/jctb.2000.1989 10.1145/285055.285059 10.1145/1374376.1374389 10.1137/1.9781611973082.83 10.1287/moor.2016.0809 10.1145/502090.502096 10.1609/aaai.v29i1.9486 10.1137/090779346 10.1137/130929205 10.1137/1.9781611973730.80 10.1007/BF02579273 10.1007/s00453-020-00757-9 10.1109/FOCS.2011.46 10.1137/110832318 10.1145/3447548.3467367 10.1287/moor.3.3.177 10.1016/j.geb.2005.02.006 10.1137/080733991 |
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| Snippet | 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... In this paper, we present a thorough study of the regularized submodular maximization problem, in which the objective f:=g−ℓ can be expressed as the difference... |
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| SubjectTerms | Algorithms Constraints continuous greedy algorithm Greedy algorithms Maximization Optimization random greedy algorithm regularized problem sampling Submodular maximization Weighting |
| Title | Regularized nonmonotone submodular maximization |
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