# Distributed Gradient Descent for Functional Learning

arXiv: https://arxiv.org/abs/2305.07408 · HTML: https://mlsanity.com/paper/2305.07408/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 12 May 2023.

## Builds on (most cited first, 20 of 20)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Learning Theory for Distribution Regression](https://mlsanity.com/paper/1411.2066/) (2014)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Information Theory with Kernel Methods](https://mlsanity.com/paper/2202.08545/) (2022)
- [Parsimonious Online Learning with Kernels via Sparse Projections in Function Space](https://mlsanity.com/paper/1612.04111/) (2016)
- [Distributed Online Linear Regression](https://mlsanity.com/paper/1902.04774/) (2019)
- [Capacity dependent analysis for functional online learning algorithms](https://mlsanity.com/paper/2209.12198/) (2022)
- [Decentralised Learning with Random Features and Distributed Gradient Descent](https://mlsanity.com/paper/2007.00360/) (2020)
- [COKE: Communication-Censored Decentralized Kernel Learning](https://mlsanity.com/paper/2001.10133/) (2020)
- [Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression](https://mlsanity.com/paper/2211.10968/) (2022)
- [Fast and Strong Convergence of Online Learning Algorithms](https://mlsanity.com/paper/1710.03600/) (2017)
- [Decentralized Online Learning with Kernels](https://mlsanity.com/paper/1710.04062/) (2017)
- [Distributed filtered hyperinterpolation for noisy data on the sphere](https://mlsanity.com/paper/1910.02434/) (2019)
- [Robust Kernel-based Distribution Regression](https://mlsanity.com/paper/2104.10637/) (2021)
- [Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization](https://mlsanity.com/paper/1903.04157/) (2019)
- [Distributed Learning with Dependent Samples](https://mlsanity.com/paper/2002.03757/) (2020)
- [Optimal Rates of Distributed Regression with Imperfect Kernels](https://mlsanity.com/paper/2006.16744/) (2020)
- [Online Regularized Learning Algorithm for Functional Data](https://mlsanity.com/paper/2211.13549/) (2022)

## Built on by (most cited first, 2 of 2)

- [Theory of Decentralized Robust Kernel-Based Learning](https://mlsanity.com/paper/2506.05215/) (2025)
- [Generalization Analysis of Distributed Kernel-based Robust Gradient Descent Algorithms](https://mlsanity.com/paper/2609.11712/) (2026)

## Abstract (arXiv)

In recent years, different types of distributed and parallel learning schemes have received increasing attention for their strong advantages in handling large-scale data information. In the information era, to face the big data challenges {that} stem from functional data analysis very recently, we propose a novel distributed gradient descent functional learning (DGDFL) algorithm to tackle functional data across numerous local machines (processors) in the framework of reproducing kernel Hilbert space. Based on integral operator approaches, we provide the first theoretical understanding of the DGDFL algorithm in many different aspects of the literature. On the way of understanding DGDFL, firstly, a data-based gradient descent functional learning (GDFL) algorithm associated with a single-machine model is proposed and comprehensively studied. Under mild conditions, confidence-based optimal learning rates of DGDFL are obtained without the saturation boundary on the regularity index suffered in previous works in functional regression. We further provide a semi-supervised DGDFL approach to weaken the restriction on the maximal number of local machines to ensure optimal rates. To our best knowledge, the DGDFL provides the first divide-and-conquer iterative training approach to functional learning based on data samples of intrinsically infinite-dimensional random functions (functional covariates) and enriches the methodologies for functional data analysis.