# Decentralised Learning with Random Features and Distributed Gradient Descent

arXiv: https://arxiv.org/abs/2007.00360 · HTML: https://mlsanity.com/paper/2007.00360/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 9 of 9)

- [Decentralized and Model-Free Federated Learning: Consensus-Based Distillation in Function Space](https://mlsanity.com/paper/2104.00352/) (2021)
- [Distributed Learning Systems with First-order Methods](https://mlsanity.com/paper/2104.05245/) (2021)
- [On Generalization of Decentralized Learning with Separable Data](https://mlsanity.com/paper/2209.07116/) (2022)
- [Network Gradient Descent Algorithm for Decentralized Federated Learning](https://mlsanity.com/paper/2205.08364/) (2022)
- [QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM](https://mlsanity.com/paper/2208.02777/) (2022)
- [Distributed Gradient Descent for Functional Learning](https://mlsanity.com/paper/2305.07408/) (2023)
- [Decentralized Entropic Optimal Transport for Distributed Distribution Comparison](https://mlsanity.com/paper/2301.12065/) (2023)
- [Decentralized Kernel Ridge Regression Based on Data-Dependent Random Feature](https://mlsanity.com/paper/2405.07791/) (2024)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)

## Abstract (arXiv)

We investigate the generalisation performance of Distributed Gradient Descent with Implicit Regularisation and Random Features in the homogenous setting where a network of agents are given data sampled independently from the same unknown distribution. Along with reducing the memory footprint, Random Features are particularly convenient in this setting as they provide a common parameterisation across agents that allows to overcome previous difficulties in implementing Decentralised Kernel Regression. Under standard source and capacity assumptions, we establish high probability bounds on the predictive performance for each agent as a function of the step size, number of iterations, inverse spectral gap of the communication matrix and number of Random Features. By tuning these parameters, we obtain statistical rates that are minimax optimal with respect to the total number of samples in the network. The algorithm provides a linear improvement over single machine Gradient Descent in memory cost and, when agents hold enough data with respect to the network size and inverse spectral gap, a linear speed-up in computational runtime for any network topology. We present simulations that show how the number of Random Features, iterations and samples impact predictive performance.