A General Framework to Distribute Iterative Algorithms with Localized Information over Networks

• Published in: IEEE transactions on automatic control Vol. 68; no. 12; pp. 1 - 16
• Main Authors: Timoudas, Thomas Ohlson, Zhang, Silun, Magnusson, Sindri, Fischione, Carlo
• Format: Journal Article
• Language: English
• Published: New York IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Agent and autonomous system; Agents and autonomous systems; Algorithms; Centralised; communication networks; Communications networks; Computer and Systems Sciences; Convergence; data- och systemvetenskap; Distributed algorithms; Distributed computer systems; Edge computing; Gradient-descent; Heuristic algorithms; Heuristic methods; Heuristics algorithm; Internet of Things; Iterative algorithm; Iterative algorithms; Iterative methods; Learning systems; Machine learning; Newton method; Newton methods; Newton's methods; Newton-Raphson method; Number theory; Optimisations; Optimization; optimization algorithms; Parallel algorithms
• ISSN: 0018-9286; 1558-2523; 1558-2523
• DOI: 10.1109/TAC.2023.3279901

Emerging applications in IoT (Internet of Things) and edge computing/learning have sparked massive renewed interest in developing distributed versions of existing (centralized) iterative algorithms often used for optimization or machine learning purposes. While existing work in the literature exhibit similarities, for the tasks of both algorithm design and theoretical analysis, there is still no unified method or framework for accomplishing these tasks. This paper develops such a general framework, for distributing the execution of (centralized) iterative algorithms over networks in which the required information or data is partitioned between the nodes in the network. This paper furthermore shows that the distributed iterative algorithm, which results from the proposed framework, retains the convergence properties (rate) of the original (centralized) iterative algorithm. In addition, this paper applies the proposed general framework to several interesting example applications, obtaining results comparable to the state of the art for each such example, while greatly simplifying and generalizing their convergence analysis. These example applications reveal new results for distributed proximal versions of gradient descent, the heavy-ball method, and Newton's method. For example, these results show that the dependence on the condition number for the convergence rate of this distributed Heavy ball method is at least as good as for centralized gradient descent.