# Compressed Decentralized Proximal Stochastic Gradient Method for Nonconvex Composite Problems with Heterogeneous Data

arXiv: https://arxiv.org/abs/2302.14252 · HTML: https://mlsanity.com/paper/2302.14252/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2023.

## Built on by (most cited first, 11 of 11)

- [Convergence and Privacy of Decentralized Nonconvex Optimization with Gradient Clipping and Communication Compression](https://mlsanity.com/paper/2305.09896/) (2023)
- [Towards Faster Decentralized Stochastic Optimization with Communication Compression](https://mlsanity.com/paper/2405.20114/) (2024)
- [FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Data](https://mlsanity.com/paper/2504.11903/) (2025)
- [Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization](https://mlsanity.com/paper/2508.04950/) (2025)
- [Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functions](https://mlsanity.com/paper/2403.11565/) (2024)
- [DP-CSGP: Differentially Private Stochastic Gradient Push with Compressed Communication](https://mlsanity.com/paper/2512.13583/) (2025)
- [Compressed and Sparse Models for Non-Convex Decentralized Learning](https://mlsanity.com/paper/2311.05760/) (2023)
- [Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum](https://mlsanity.com/paper/2504.12742/) (2025)
- [LoDAdaC: a unified local training-based decentralized framework with adaptive gradients and compressed communication](https://mlsanity.com/paper/2604.09970/) (2026)
- [Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2607.01755/) (2026)
- [A Unified Framework for Fair and Personalized Decentralized Learning under Communication Constraints](https://mlsanity.com/paper/2608.26493/) (2026)

## Abstract (arXiv)

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save communication cost, we then extend DProxSGT to a compressed method by compressing the communicated information. Both methods need only O(1) samples per worker for each proximal update, which is important to achieve good generalization performance on training deep neural networks. With a smoothness condition on the expected loss function (but not on each sample function), the proposed methods can achieve an optimal sample complexity result to produce a near-stationary point. Numerical experiments on training neural networks demonstrate the significantly better generalization performance of our methods over large-batch training methods and momentum variance-reduction methods and also, the ability of handling heterogeneous data by the gradient tracking scheme.