# A Variance-Reduced Aggregation Based Gradient Tracking method for Distributed Optimization over Directed Networks

arXiv: https://arxiv.org/abs/2307.14776 · HTML: https://mlsanity.com/paper/2307.14776/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2023.

## 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)

This paper studies the distributed optimization problem over directed networks with noisy information-sharing. To resolve the imperfect communication issue over directed networks, a series of noise-robust variants of Push-Pull/AB method have been developed. These methods improve the robustness of Push-Pull method against the information-sharing noise through adding small factors on weight matrices and replacing the global gradient tracking with the cumulative gradient tracking. Based on the two techniques, we propose a new variant of the Push-Pull method by presenting a novel mechanism of inter-agent information aggregation, named variance-reduced aggregation (VRA). VRA helps us to release some conditions on the objective function and networks. When the objective function is convex and the sharing-information noise is variance-unbounded, it can be shown that the proposed method converges to the optimal solution almost surely. When the objective function is strongly convex and the sharing-information noise is variance-bounded, the proposed method achieves the convergence rate of Oleft(k-(1-ε)right) in the mean square sense, where ε could be close to 0 infinitely. Simulated experiments on ridge regression problems verify the effectiveness of the proposed method.