# Nested Distributed Gradient Methods with Adaptive Quantized Communication

arXiv: https://arxiv.org/abs/1903.08149 · HTML: https://mlsanity.com/paper/1903.08149/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks](https://mlsanity.com/paper/2106.07243/) (2021)
- [Quantization enabled Privacy Protection in Decentralized Stochastic Optimization](https://mlsanity.com/paper/2208.04845/) (2022)
- [Adaptive Consensus: A network pruning approach for decentralized optimization](https://mlsanity.com/paper/2309.02626/) (2023)

## Abstract (arXiv)

In this paper, we consider minimizing a sum of local convex objective functions in a distributed setting, where communication can be costly. We propose and analyze a class of nested distributed gradient methods with adaptive quantized communication (NEAR-DGD+Q). We show the effect of performing multiple quantized communication steps on the rate of convergence and on the size of the neighborhood of convergence, and prove R-Linear convergence to the exact solution with increasing number of consensus steps and adaptive quantization. We test the performance of the method, as well as some practical variants, on quadratic functions, and show the effects of multiple quantized communication steps in terms of iterations/gradient evaluations, communication and cost.