# A One-shot Framework for Distributed Clustered Learning in Heterogeneous Environments

arXiv: https://arxiv.org/abs/2209.10866 · HTML: https://mlsanity.com/paper/2209.10866/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 69 references that are in the map.
- First posted on arXiv 22 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Generalizing from a Few Examples: A Survey on Few-Shot Learning](https://mlsanity.com/paper/1904.05046/) (2019)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Salvaging Federated Learning by Local Adaptation](https://mlsanity.com/paper/2002.04758/) (2020)
- [One-Shot Federated Learning](https://mlsanity.com/paper/1902.11175/) (2019)
- [Distilled One-Shot Federated Learning](https://mlsanity.com/paper/2009.07999/) (2020)
- [Robust Federated Learning in a Heterogeneous Environment](https://mlsanity.com/paper/1906.06629/) (2019)
- [Heterogeneity for the Win: One-Shot Federated Clustering](https://mlsanity.com/paper/2103.00697/) (2021)
- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [Simple and optimal high-probability bounds for strongly-convex stochastic gradient descent](https://mlsanity.com/paper/1909.00843/) (2019)
- [Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm](https://mlsanity.com/paper/1810.02677/) (2018)
- [The Accented English Speech Recognition Challenge 2020: Open Datasets, Tracks, Baselines, Results and Methods](https://mlsanity.com/paper/2102.10233/) (2021)
- [One-Shot Federated Learning: Theoretical Limits and Algorithms to Achieve Them](https://mlsanity.com/paper/1905.04634/) (2019)
- [Empirical Risk Minimization for Stochastic Convex Optimization: O(1/n)- and O(1/n2)-type of Risk Bounds](https://mlsanity.com/paper/1702.02030/) (2017)
- [Personalized Federated Learning via Convex Clustering](https://mlsanity.com/paper/2202.00718/) (2022)
- [Gradient Based Clustering](https://mlsanity.com/paper/2202.00720/) (2022)
- [FedBC: Calibrating Global and Local Models via Federated Learning Beyond Consensus](https://mlsanity.com/paper/2206.10815/) (2022)

## Built on by (most cited first, 3 of 3)

- [FedPNN: One-shot Federated Classification via Evolving Clustering Method and Probabilistic Neural Network hybrid](https://mlsanity.com/paper/2304.04147/) (2023)
- [A Unified Framework for Center-based Clustering of Distributed Data](https://mlsanity.com/paper/2402.01302/) (2024)
- [Distributed Gradient Clustering: Convergence and the Effect of Initialization](https://mlsanity.com/paper/2603.20507/) (2026)

## Abstract (arXiv)

The paper proposes a family of communication efficient methods for distributed learning in heterogeneous environments in which users obtain data from one of K different distributions. In the proposed setup, the grouping of users (based on the data distributions they sample), as well as the underlying statistical properties of the distributions, are apriori unknown. A family of One-shot Distributed Clustered Learning methods (ODCL-C) is proposed, parametrized by the set of admissible clustering algorithms C, with the objective of learning the true model at each user. The admissible clustering methods include K-means (KM) and convex clustering (CC), giving rise to various one-shot methods within the proposed family, such as ODCL-KM and ODCL-CC. The proposed one-shot approach, based on local computations at the users and a clustering based aggregation step at the server is shown to provide strong learning guarantees. In particular, for strongly convex problems it is shown that, as long as the number of data points per user is above a threshold, the proposed approach achieves order-optimal mean-squared error (MSE) rates in terms of the sample size. An explicit characterization of the threshold is provided in terms of problem parameters. The trade-offs with respect to selecting various clustering methods (ODCL-CC, ODCL-KM) are discussed and significant improvements over state-of-the-art are demonstrated. Numerical experiments illustrate the findings and corroborate the performance of the proposed methods.