# Optimizing Stochastic Gradient Push under Broadcast Communications

arXiv: https://arxiv.org/abs/2604.15549 · HTML: https://mlsanity.com/paper/2604.15549/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [Stochastic Gradient Push for Distributed Deep Learning](https://mlsanity.com/paper/1811.10792/) (2018)
- [Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-Update SGD](https://mlsanity.com/paper/1810.08313/) (2018)
- [Optimal Complexity in Decentralized Training](https://mlsanity.com/paper/2006.08085/) (2020)
- [Decentralized gradient methods: does topology matter?](https://mlsanity.com/paper/2002.12688/) (2020)
- [Refined Convergence and Topology Learning for Decentralized SGD with Heterogeneous Data](https://mlsanity.com/paper/2204.04452/) (2022)
- [SQuARM-SGD: Communication-Efficient Momentum SGD for Decentralized Optimization](https://mlsanity.com/paper/2005.07041/) (2020)
- [Beyond spectral gap: The role of the topology in decentralized learning](https://mlsanity.com/paper/2206.03093/) (2022)
- [A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2102.06752/) (2021)
- [Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions](https://mlsanity.com/paper/1811.03982/) (2018)
- [Decentralized Learning over Wireless Networks: The Effect of Broadcast with Random Access](https://mlsanity.com/paper/2305.07368/) (2023)
- [Adaptive Weighting Push-SUM for Decentralized Optimization with Statistical Diversity](https://mlsanity.com/paper/2412.07252/) (2024)
- [Stochastic Push-Pull for Decentralized Nonconvex Optimization](https://mlsanity.com/paper/2506.07021/) (2025)

## Abstract (arXiv)

We consider the problem of minimizing the convergence time for decentralized federated learning (DFL) in wireless networks under broadcast communications, with focus on mixing matrix design. The mixing matrix is a critical hyperparameter for DFL that simultaneously controls the convergence rate across iterations and the communication demand per iteration, both strongly influencing the convergence time. Although the problem has been studied previously, existing solutions are mostly designed for decentralized parallel stochastic gradient descent (D-PSGD), which requires the mixing matrix to be symmetric and doubly stochastic. These constraints confine the activated communication graph to undirected (i.e., bidirected) graphs, which limits design flexibility. In contrast, we consider mixing matrix design for stochastic gradient push (SGP), which allows asymmetric mixing matrices and hence directed communication graphs. By analyzing how the convergence rate of SGP depends on the mixing matrices, we extract an objective function that explicitly depends on graph-theoretic parameters of the activated communication graph, based on which we develop an efficient design algorithm with performance guarantees. Our evaluations based on real data show that the proposed solution can notably reduce the convergence time compared to the state of the art without compromising the quality of the trained model.