A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization
Based on the idea of randomized coordinate descent of α-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and...
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| Vydáno v: | IEEE transactions on automatic control Ročník 61; číslo 10; s. 2947 - 2957 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.10.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
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| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | Based on the idea of randomized coordinate descent of α-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and Condat that includes the well-known Alternating Direction Method of Multipliers as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates. |
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| AbstractList | Based on the idea of randomized coordinate descent of [Formula Omitted]-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vu and Condat that includes the well-known Alternating Direction Method of Multipliers as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates. Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and Condat that includes the well known ADMM as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates. Based on the idea of randomized coordinate descent of α-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by Vũ and Condat that includes the well-known Alternating Direction Method of Multipliers as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates. |
| Author | Iutzeler, Franck Hachem, Walid Bianchi, Pascal |
| Author_xml | – sequence: 1 givenname: Pascal surname: Bianchi fullname: Bianchi, Pascal email: pascal.bianchi@telecom-paristech.fr organization: LTCI, Telecom ParisTech, Paris, France – sequence: 2 givenname: Walid surname: Hachem fullname: Hachem, Walid email: walid.hachem@telecom-paristech.fr organization: LTCI, Telecom ParisTech, Paris, France – sequence: 3 givenname: Franck surname: Iutzeler fullname: Iutzeler, Franck email: franck.iutzeler@imag.fr organization: LJK, Univ. Grenoble Alpes, Grenoble, France |
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| SubjectTerms | Consensus algorithms Convergence Convex functions coordinate descent Cost function distributed optimization Mathematics Minimization Optimization algorithms Optimization and Control primal-dual algorithm Statistics Yttrium |
| Title | A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization |
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