# Quantized Consensus by the ADMM: Probabilistic versus Deterministic Quantizers

arXiv: https://arxiv.org/abs/1502.01053 · HTML: https://mlsanity.com/paper/1502.01053/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2015.

## Built on by (most cited first, 5 of 5)

- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [Communication efficient privacy-preserving distributed optimization using adaptive differential quantization](https://mlsanity.com/paper/2105.14416/) (2021)
- [Decentralized Multi-Task Stochastic Optimization With Compressed Communications](https://mlsanity.com/paper/2112.12373/) (2021)
- [Sparsity-Aware Distributed Learning for Gaussian Processes with Linear Multiple Kernel](https://mlsanity.com/paper/2309.08201/) (2023)
- [Limited Communications Distributed Optimization via Deep Unfolded Distributed ADMM](https://mlsanity.com/paper/2309.14353/) (2023)

## Abstract (arXiv)

This paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers (ADMM). We first study the effects of probabilistic and deterministic quantizations on a distributed ADMM algorithm. With probabilistic quantization, this algorithm yields linear convergence to the desired average in the mean sense with a bounded variance. When deterministic quantization is employed, the distributed ADMM either converges to a consensus or cycles with a finite period after a finite-time iteration. In the cyclic case, local quantized variables have the same mean over one period and hence each node can also reach a consensus. We then obtain an upper bound on the consensus error which depends only on the quantization resolution and the average degree of the network. Finally, we propose a two-stage algorithm which combines both probabilistic and deterministic quantizations. Simulations show that the two-stage algorithm, without picking small algorithm parameter, has consensus errors that are typically less than one quantization resolution for all connected networks where agents' data can be of arbitrary magnitudes.