# Quantization Design for Distributed Optimization

arXiv: https://arxiv.org/abs/1504.02317 · HTML: https://mlsanity.com/paper/1504.02317/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2015.

## Built on by (most cited first, 4 of 4)

- [Quantization enabled Privacy Protection in Decentralized Stochastic Optimization](https://mlsanity.com/paper/2208.04845/) (2022)
- [Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data](https://mlsanity.com/paper/2406.00621/) (2024)
- [Communication-Efficient Federated Linear and Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2109.12400/) (2021)
- [Quantized Stochastic Primal-Dual Methods for Distributed Optimization under Relaxed Global Geometry](https://mlsanity.com/paper/2606.11339/) (2026)

## Abstract (arXiv)

We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a limited data-rate. A common technique to address the latter limitation is to apply quantization to the exchanged information. We propose two distributed optimization algorithms with an iteratively refining quantization design based on the inexact proximal gradient method and its accelerated variant. We show that if the parameters of the quantizers, i.e. the number of bits and the initial quantization intervals, satisfy certain conditions, then the quantization error is bounded by a linearly decreasing function and the convergence of the distributed algorithms is guaranteed. Furthermore, we prove that after imposing the quantization scheme, the distributed algorithms still exhibit a linear convergence rate, and show complexity upper-bounds on the number of iterations to achieve a given accuracy. Finally, we demonstrate the performance of the proposed algorithms and the theoretical findings for solving a distributed optimal control problem.