# A Linearly Convergent Robust Compressed Push-Pull Method for Decentralized Optimization

arXiv: https://arxiv.org/abs/2303.07091 · HTML: https://mlsanity.com/paper/2303.07091/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2023.

## Built on by (most cited first, 2 of 2)

- [Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression](https://mlsanity.com/paper/2305.09896/) (2023)
- [DP-CSGP: Differentially Private Stochastic Gradient Push with Compressed Communication](https://mlsanity.com/paper/2512.13583/) (2025)

## Abstract (arXiv)

In the modern paradigm of multi-agent networks, communication has become one of the main bottlenecks for decentralized optimization, where a large number of agents are involved in minimizing the average of the local cost functions. In this paper, we propose a robust compressed push-pull algorithm (RCPP) that combines gradient tracking with communication compression. In particular, RCPP is compatible with a much more general class of compression operators that allow both relative and absolute compression errors. We show that RCPP achieves linear convergence rate for smooth objective functions satisfying the Polyak-Lojasiewicz condition over general directed networks. Numerical examples verify the theoretical findings and demonstrate the efficiency, flexibility, and robustness of the proposed algorithm.