# Automated Performance Estimation for Decentralized Optimization via Network Size Independent Problems

arXiv: https://arxiv.org/abs/2210.00695 · HTML: https://mlsanity.com/paper/2210.00695/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2022.

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

- [Federated Learning for Financial Forecasting](https://mlsanity.com/paper/2509.16393/) (2025)

## Abstract (arXiv)

We develop a novel formulation of the Performance Estimation Problem (PEP) for decentralized optimization whose size is independent of the number of agents in the network. The PEP approach allows computing automatically the worst-case performance and worst-case instance of first-order optimization methods by solving an SDP. Unlike previous work, the size of our new PEP formulation is independent of the network size. For this purpose, we take a global view of the decentralized problem and we also decouple the consensus subspace and its orthogonal complement. We apply our methodology to different decentralized methods such as DGD, DIGing and EXTRA and obtain numerically tight performance guarantees that are valid for any network size.