# Optimality in Decentralized Optimization under Bandwidth Constraints

arXiv: https://arxiv.org/abs/2603.20735 · HTML: https://mlsanity.com/paper/2603.20735/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2026.

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

- [Decentralized Optimization with Cross-Coupled Mixed Affine Constraints](https://mlsanity.com/paper/2609.33021/) (2026)

## Abstract (arXiv)

We consider a realistic decentralized setup with bandwidth-constrained communication and derive optimal time complexities for non-convex stochastic parallel and asynchronous optimization (up to logarithmic factors). We develop the corresponding methods, Grace SGD and Leon SGD, for both homogeneous and heterogeneous settings. Unlike previous work, our optimal bounds are characterized in terms of min-cut/max-flow quantities and rely on tools from Gomory-Hu trees and Steiner Tree Packing problems, providing tighter and more practical complexities.