# A Robust Gradient Tracking Method for Distributed Optimization over Directed Networks

arXiv: https://arxiv.org/abs/2003.13980 · HTML: https://mlsanity.com/paper/2003.13980/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2020.

## Built on by (most cited first, 7 of 7)

- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Zero-Order One-Point Estimate with Distributed Stochastic Gradient-Tracking Technique](https://mlsanity.com/paper/2210.05618/) (2022)
- [Robust Fully-Asynchronous Methods for Distributed Training over General Architecture](https://mlsanity.com/paper/2307.11617/) (2023)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [Online Distributed Learning with Quantized Finite-Time Coordination](https://mlsanity.com/paper/2307.06620/) (2023)
- [Single Point-Based Distributed Zeroth-Order Optimization with a Non-Convex Stochastic Objective Function](https://mlsanity.com/paper/2410.05942/) (2024)
- [A Weighted Gradient Tracking Privacy-Preserving Method for Distributed Optimization](https://mlsanity.com/paper/2509.18134/) (2025)

## Abstract (arXiv)

In this paper, we consider the problem of distributed consensus optimization over multi-agent networks with directed network topology. Assuming each agent has a local cost function that is smooth and strongly convex, the global objective is to minimize the average of all the local cost functions. To solve the problem, we introduce a robust gradient tracking method (R-Push-Pull) adapted from the recently proposed Push-Pull/AB algorithm. R-Push-Pull inherits the advantages of Push-Pull and enjoys linear convergence to the optimal solution with exact communication. Under noisy information exchange, R-Push-Pull is more robust than the existing gradient tracking based algorithms; the solutions obtained by each agent reach a neighborhood of the optimum in expectation exponentially fast under a constant stepsize policy. We provide a numerical example that demonstrate the effectiveness of R-Push-Pull.