Application of multi-agent systems in distributed optimization problems

This paper systematizes and provides a detailed analysis of modern distributed optimization methods in multi-agent systems (MAS). Multi-agent approaches, defined as a set of interacting autonomous computing entities, are becoming critically in demand when centralized data processing is impossible due to the scale of problems, strict response time requirements, or the need to ensure the privacy of local information. The goal of the work is to comprehensively investigate key approaches to decentralized optimization and identify the fundamental factors that determine their computational efficiency, fault tolerance, and practical applicability. Within the framework of the study, five main classes of algorithms are considered in detail: consensus gradient descent (DGD), gradient tracking methods, the distributed alternating direction method of multipliers (ADMM), as well as modern stochastic and communication-efficient approaches, including Local SGD and FedAvg. The paper thoroughly analyzes systemic limitations imposed by the connectivity graph topology, data compression algorithms, and strict differential privacy requirements. Key theoretical and practical aspects of constructing optimal procedures based on a balanced combination of network architecture, the nature of local cost functions, and available communication channel bandwidth are revealed. Recommendations for choosing specific algorithmic solutions depending on the specifics of the application environment are formulated.

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