# Federated Frank-Wolfe Algorithm

arXiv: https://arxiv.org/abs/2408.10090 · HTML: https://mlsanity.com/paper/2408.10090/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 54 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 30 of 39)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [Minibatch vs Local SGD for Heterogeneous Distributed Learning](https://mlsanity.com/paper/2006.04735/) (2020)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [FedSplit: An algorithmic framework for fast federated optimization](https://mlsanity.com/paper/2005.05238/) (2020)
- [Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization](https://mlsanity.com/paper/1910.13598/) (2019)
- [Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms](https://mlsanity.com/paper/2010.05273/) (2020)
- [Auditing Privacy Defenses in Federated Learning via Generative Gradient Leakage](https://mlsanity.com/paper/2203.15696/) (2022)
- [Convergence Rate of Frank-Wolfe for Non-Convex Objectives](https://mlsanity.com/paper/1607.00345/) (2016)
- [Federated Composite Optimization](https://mlsanity.com/paper/2011.08474/) (2020)
- [Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximization](https://mlsanity.com/paper/1804.09554/) (2018)
- [Stochastic Frank-Wolfe Methods for Nonconvex Optimization](https://mlsanity.com/paper/1607.08254/) (2016)
- [Variance-Reduced and Projection-Free Stochastic Optimization](https://mlsanity.com/paper/1602.02101/) (2016)
- [FedADMM: A Federated Primal-Dual Algorithm Allowing Partial Participation](https://mlsanity.com/paper/2203.15104/) (2022)
- [FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimization](https://mlsanity.com/paper/2103.03452/) (2021)
- [New Analysis and Results for the Frank-Wolfe Method](https://mlsanity.com/paper/1307.0873/) (2013)
- [A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming](https://mlsanity.com/paper/1804.08544/) (2018)
- [Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization](https://mlsanity.com/paper/2002.11860/) (2020)
- [Decentralized Submodular Maximization: Bridging Discrete and Continuous Settings](https://mlsanity.com/paper/1802.03825/) (2018)
- [Fast Composite Optimization and Statistical Recovery in Federated Learning](https://mlsanity.com/paper/2207.08204/) (2022)
- [Decentralized Frank-Wolfe Algorithm for Convex and Non-convex Problems](https://mlsanity.com/paper/1612.01216/) (2016)

## Abstract (arXiv)

Federated learning (FL) has gained a lot of attention in recent years for building privacy-preserving collaborative learning systems. However, FL algorithms for constrained machine learning problems are still limited, particularly when the projection step is costly. To this end, we propose a Federated Frank-Wolfe Algorithm (FedFW). FedFW features data privacy, low per-iteration cost, and communication of sparse signals. In the deterministic setting, FedFW achieves an varepsilon-suboptimal solution within O(varepsilon-2) iterations for smooth and convex objectives, and O(varepsilon-3) iterations for smooth but non-convex objectives. Furthermore, we present a stochastic variant of FedFW and show that it finds a solution within O(varepsilon-3) iterations in the convex setting. We demonstrate the empirical performance of FedFW on several machine learning tasks.