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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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 70; no. 5; pp. 3433 - 3440
Main Authors: Shahriari-Mehr, Firooz, Panahi, Ashkan
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:0018-9286, 1558-2523, 1558-2523
Online Access:Get full text
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Summary: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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content type line 14
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2024.3520513