# Efficient Gradient Tracking Algorithms for Distributed Optimization Problems with Inexact Communication

arXiv: https://arxiv.org/abs/2501.05737 · HTML: https://mlsanity.com/paper/2501.05737/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2025.

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

- [Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm](https://mlsanity.com/paper/2606.22466/) (2026)

## Abstract (arXiv)

Distributed optimization problems usually face inexact communication issues induced by channel noise, communication quantization or differential privacy protection. Most existing algorithms need a two-timescale setting of the stepsize of gradient descent and the parameter of noise suppression to ensure the convergence to the optimal solution. In this paper, we propose two single-timescale algorithms, VRA-DGT and VRA-DSGT, for distributed deterministic and stochastic optimization problems with inexact communication respectively. VRA-DGT integrates the Variance-Reduced Aggregation (VRA) mechanism with the distributed gradient tracking framework, which achieves the convergence rate of Oleft(k-1right) in the mean square sense and Oleft(fracln(k+1)kbright), forall b∈(0.5,1) in the almost sure sense when the objective function is strongly convex and smooth. For stochastic optimization problems, VRA-DSGT, where a hybrid variance-reduced technique has been introduced in VRA-DGT, maintains the convergence rate of Oleft(k-1right) in the mean square sense and Oleft(fracln(k+1)kbright), forall b∈(0.5,1) in the almost sure sense. Simulated experiments on a logistic regression problem with real-world data verify the effectiveness of the proposed algorithms.