Double Averaging and Gradient Projection: Convergence Guarantees for Decentralized Constrained Optimization
We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set. For this setup, we propose a novel decentralized algorithm,...
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| Vydané v: | IEEE transactions on automatic control Ročník 70; číslo 5; s. 3433 - 3440 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
IEEE
01.05.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9286, 1558-2523, 1558-2523 |
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| Abstract | We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set. For this setup, we propose a novel decentralized algorithm, called double averaging and gradient projection (DAGP). We achieve global optimality through a novel distributed tracking technique we call distributed null projection. Further, we show that DAGP can be used to solve unconstrained problems with nondifferentiable objective terms with a problem reduction scheme. Assuming only smoothness of the objective terms, we study the convergence of DAGP and establish sublinear rates of convergence in terms of feasibility, consensus, and optimality, with no extra assumption (e.g., strong convexity). For the analysis, we forego the difficulties of selecting Lyapunov functions by proposing a new methodology of convergence analysis, which we refer to as aggregate lower-bounding. To demonstrate the generality of this method, we also provide an alternative convergence proof for the standard gradient descent algorithm with smooth functions. |
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| AbstractList | We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set. For this setup, we propose a novel decentralized algorithm, called double averaging and gradient projection (DAGP). We achieve global optimality through a novel distributed tracking technique we call distributed null projection. Further, we show that DAGP can be used to solve unconstrained problems with nondifferentiable objective terms with a problem reduction scheme. Assuming only smoothness of the objective terms, we study the convergence of DAGP and establish sublinear rates of convergence in terms of feasibility, consensus, and optimality, with no extra assumption (e.g., strong convexity). For the analysis, we forego the difficulties of selecting Lyapunov functions by proposing a new methodology of convergence analysis, which we refer to as aggregate lower-bounding. To demonstrate the generality of this method, we also provide an alternative convergence proof for the standard gradient descent algorithm with smooth functions. We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set. For this setup, we propose a novel decentralized algorithm, called DAGP (Double Averaging and Gradient Projection). We achieve global optimality through a novel distributed tracking technique we call distributed null projection. Further, we show that DAGP can be used to solve unconstrained problems with non-differentiable objective terms with a problem reduction scheme. Assuming only smoothness of the objective terms, we study the convergence of DAGP and establish sub-linear rates of convergence in terms of feasibility, consensus, and optimality, with no extra assumption (e.g. strong convexity). For the analysis, we forego the difficulties of selecting Lyapunov functions by proposing a new methodology of convergence analysis, which we refer to as aggregate lower-bounding. To demonstrate the generality of this method, we also provide an alternative convergence proof for the standard gradient descent algorithm with smooth functions. |
| Author | Shahriari-Mehr, Firooz Panahi, Ashkan |
| Author_xml | – sequence: 1 givenname: Firooz orcidid: 0000-0003-2374-2341 surname: Shahriari-Mehr fullname: Shahriari-Mehr, Firooz email: firooz@chalmers.se organization: Department of Computer Science and Engineering, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden – sequence: 2 givenname: Ashkan orcidid: 0000-0003-2085-7127 surname: Panahi fullname: Panahi, Ashkan email: ashkan.panahi@chalmers.se organization: Department of Computer Science and Engineering, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden |
| BackLink | https://gup.ub.gu.se/publication/350004$$DView record from Swedish Publication Index (Göteborgs universitet) https://research.chalmers.se/publication/544526$$DView record from Swedish Publication Index (Chalmers tekniska högskola) |
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| References | ref13 ref35 ref12 ref15 ref37 ref14 ref36 Forero (ref38) 2010; 11 ref31 ref30 ref11 ref33 ref10 ref32 ref2 ref1 ref39 ref16 ref19 Wang (ref34) 2015 Shahriari-Mehr (ref43) 2023 Tsianos (ref18) 2012; 25 ref24 ref23 ref26 ref25 ref20 ref42 ref41 ref22 ref21 ref28 ref27 Bishop (ref6) 2006 ref29 Calafiore (ref40) 2014 ref8 ref7 ref9 ref4 ref3 ref5 Ram (ref17) 2010; 147 Beck (ref44) 2010 |
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| SubjectTerms | Algorithms Communication networks Computer architecture Computer Sciences Constrained optimization Constraints Convergence convergence analysis Convex functions convex optimization Convexity Datavetenskap (datalogi) Directed graphs distributed optimization Liapunov functions Linear programming Lyapunov methods Networked, Parallel and Distributed Computing Nätverks-, parallell- och distribuerad beräkning Optimization Optimization methods Smoothness Vectors |
| Title | Double Averaging and Gradient Projection: Convergence Guarantees for Decentralized Constrained Optimization |
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