# Logarithmically Quantized Distributed Optimization over Dynamic Multi-Agent Networks

arXiv: https://arxiv.org/abs/2410.20345 · HTML: https://mlsanity.com/paper/2410.20345/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 27 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Convolutional Neural Networks using Logarithmic Data Representation](https://mlsanity.com/paper/1603.01025/) (2016)
- [Deep Learning for Distributed Optimization: Applications to Wireless Resource Management](https://mlsanity.com/paper/1905.13378/) (2019)
- [S-ADDOPT: Decentralized stochastic first-order optimization over directed graphs](https://mlsanity.com/paper/2005.07785/) (2020)
- [Distributed support-vector-machine over dynamic balanced directed networks](https://mlsanity.com/paper/2104.00399/) (2021)
- [Fast-Convergent Dynamics for Distributed Allocation of Resources Over Switching Sparse Networks with Quantized Communication Links](https://mlsanity.com/paper/2012.08181/) (2020)
- [Consensus-Based Distributed Estimation in the Presence of Heterogeneous, Time-Invariant Delays](https://mlsanity.com/paper/2104.00394/) (2021)
- [Distributed Optimization over Time-varying Graphs with Imperfect Sharing of Information](https://mlsanity.com/paper/2106.08469/) (2021)
- [Optimal CPU Scheduling in Data Centers via a Finite-Time Distributed Quantized Coordination Mechanism](https://mlsanity.com/paper/2104.03126/) (2021)
- [1st-Order Dynamics on Nonlinear Agents for Resource Allocation over Uniformly-Connected Networks](https://mlsanity.com/paper/2109.04822/) (2021)
- [Gradient-tracking based Distributed Optimization with Guaranteed Optimality under Noisy Information Sharing](https://mlsanity.com/paper/2210.00551/) (2022)
- [Accelerated Distributed Allocation](https://mlsanity.com/paper/2401.15598/) (2024)
- [Distributed Optimization with Quantized Gradient Descent](https://mlsanity.com/paper/2211.10855/) (2022)
- [Distributed event-triggered coordination for average consensus on weight-balanced digraphs](https://mlsanity.com/paper/1407.7921/) (2014)

## Built on by (most cited first, 1 of 1)

- [Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs](https://mlsanity.com/paper/2506.01404/) (2025)

## Abstract (arXiv)

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.