Logarithmically Quantized Distributed Optimization over Dynamic Multi-Agent Networks
This work addresses communication constraints in multi-agent networks for applications like machine learning, but it is incremental as it builds on existing quantization techniques.
The paper tackles distributed optimization under limited bandwidth by proposing a logarithmically quantized data transmission method, which improves precision for near-optimal values and enhances algorithm accuracy compared to uniform quantization, with analysis for dynamic network topologies.
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 paper, 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.