# FedSplit: An algorithmic framework for fast federated optimization

arXiv: https://arxiv.org/abs/2005.05238 · HTML: https://mlsanity.com/paper/2005.05238/

## Key facts

- Cited by 108 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2020.

## Built on by (most cited first, 30 of 108)

- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
- [FedCM: Federated Learning with Client-level Momentum](https://mlsanity.com/paper/2106.10874/) (2021)
- [On Large-Cohort Training for Federated Learning](https://mlsanity.com/paper/2106.07820/) (2021)
- [FedVARP: Tackling the Variance Due to Partial Client Participation in Federated Learning](https://mlsanity.com/paper/2207.14130/) (2022)
- [What Do We Mean by Generalization in Federated Learning?](https://mlsanity.com/paper/2110.14216/) (2021)
- [FedNest: Federated Bilevel, Minimax, and Compositional Optimization](https://mlsanity.com/paper/2205.02215/) (2022)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [FedAvg with Fine Tuning: Local Updates Lead to Representation Learning](https://mlsanity.com/paper/2205.13692/) (2022)
- [Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning](https://mlsanity.com/paper/2103.05032/) (2021)
- [Federated Learning via Decentralized Dataset Distillation in Resource-Constrained Edge Environments](https://mlsanity.com/paper/2208.11311/) (2022)
- [Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape](https://mlsanity.com/paper/2305.11584/) (2023)
- [Sharp Bounds for Federated Averaging (Local SGD) and Continuous Perspective](https://mlsanity.com/paper/2111.03741/) (2021)
- [On Convergence of FedProx: Local Dissimilarity Invariant Bounds, Non-smoothness and Beyond](https://mlsanity.com/paper/2206.05187/) (2022)
- [FedADMM: A Federated Primal-Dual Algorithm Allowing Partial Participation](https://mlsanity.com/paper/2203.15104/) (2022)
- [SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression](https://mlsanity.com/paper/2206.09888/) (2022)
- [Local Adaptivity in Federated Learning: Convergence and Consistency](https://mlsanity.com/paper/2106.02305/) (2021)
- [Finite-Time Analysis of On-Policy Heterogeneous Federated Reinforcement Learning](https://mlsanity.com/paper/2401.15273/) (2024)
- [Architecture Agnostic Federated Learning for Neural Networks](https://mlsanity.com/paper/2202.07757/) (2022)
- [FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimization](https://mlsanity.com/paper/2103.03452/) (2021)
- [Federated Temporal Difference Learning with Linear Function Approximation under Environmental Heterogeneity](https://mlsanity.com/paper/2302.02212/) (2023)
- [Understanding Generalization of Federated Learning via Stability: Heterogeneity Matters](https://mlsanity.com/paper/2306.03824/) (2023)
- [Fed-ensemble: Improving Generalization through Model Ensembling in Federated Learning](https://mlsanity.com/paper/2107.10663/) (2021)
- [Personalized Federated Learning for Heterogeneous Clients with Clustered Knowledge Transfer](https://mlsanity.com/paper/2109.08119/) (2021)
- [The Internet of Federated Things (IoFT): A Vision for the Future and In-depth Survey of Data-driven Approaches for Federated Learning](https://mlsanity.com/paper/2111.05326/) (2021)
- [Accelerated Federated Learning with Decoupled Adaptive Optimization](https://mlsanity.com/paper/2207.07223/) (2022)
- [Efficient Federated Learning via Local Adaptive Amended Optimizer with Linear Speedup](https://mlsanity.com/paper/2308.00522/) (2023)
- [Proportional Fairness in Federated Learning](https://mlsanity.com/paper/2202.01666/) (2022)

## Abstract (arXiv)

Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication. We first study some past procedures for federated optimization, and show that their fixed points need not correspond to stationary points of the original optimization problem, even in simple convex settings with deterministic updates. In order to remedy these issues, we introduce FedSplit, a class of algorithms based on operator splitting procedures for solving distributed convex minimization with additive structure. We prove that these procedures have the correct fixed points, corresponding to optima of the original optimization problem, and we characterize their convergence rates under different settings. Our theory shows that these methods are provably robust to inexact computation of intermediate local quantities. We complement our theory with some simple experiments that demonstrate the benefits of our methods in practice.