Logarithmically Quantized Distributed Optimization Over Dynamic Multi-Agent Networks

• Published in: IEEE control systems letters Vol. 8; pp. 2433 - 2438
• Main Authors: Doostmohammadian, Mohammadreza, Pequito, Sergio
• Format: Journal Article
• Language: English
• Published: IEEE 2024
• Subjects: consensus; Convergence; Distributed databases; Distributed optimization; Eigenvalues and eigenfunctions; Heuristic algorithms; Network topology; Optimization; Perturbation methods; perturbation theory; quantization; Quantization (signal); Radio frequency; support vector machine; Support vector machines
• ISSN: 2475-1456; 2475-1456
• DOI: 10.1109/LCSYS.2024.3487796

Distributed optimization finds many applications in machine learning, signal processing, and control systems. In these real-world applications, the constraints of communication networks, particularly limited bandwidth, necessitate implementing quantization techniques. In this letter, we propose distributed optimization dynamics over multi-agent networks subject to logarithmically quantized data transmission. Under this condition, data exchange benefits from representing smaller values with more bits and larger values with fewer bits. As compared to uniform quantization, this allows for higher precision in representing near-optimal values and more accuracy of the distributed optimization algorithm. The proposed optimization dynamics comprise a primary state variable converging to the optimizer and an auxiliary variable tracking the objective function's gradient. Our setting accommodates dynamic network topologies, resulting in a hybrid system requiring convergence analysis using matrix perturbation theory and eigenspectrum analysis.