# A-FedPD: Aligning Dual-Drift is All Federated Primal-Dual Learning Needs

arXiv: https://arxiv.org/abs/2409.18915 · HTML: https://mlsanity.com/paper/2409.18915/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 63 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 30 of 45)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [Generalized Federated Learning via Sharpness Aware Minimization](https://mlsanity.com/paper/2206.02618/) (2022)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [SlowMo: Improving Communication-Efficient Distributed SGD with Slow Momentum](https://mlsanity.com/paper/1910.00643/) (2019)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [FedSplit: An algorithmic framework for fast federated optimization](https://mlsanity.com/paper/2005.05238/) (2020)
- [Improving Generalization in Federated Learning by Seeking Flat Minima](https://mlsanity.com/paper/2203.11834/) (2022)
- [FedCM: Federated Learning with Client-level Momentum](https://mlsanity.com/paper/2106.10874/) (2021)
- [From Local SGD to Local Fixed-Point Methods for Federated Learning](https://mlsanity.com/paper/2004.01442/) (2020)
- [FedVARP: Tackling the Variance Due to Partial Client Participation in Federated Learning](https://mlsanity.com/paper/2207.14130/) (2022)
- [Convergence and Accuracy Trade-Offs in Federated Learning and Meta-Learning](https://mlsanity.com/paper/2103.05032/) (2021)
- [Federated Composite Optimization](https://mlsanity.com/paper/2011.08474/) (2020)
- [FedSpeed: Larger Local Interval, Less Communication Round, and Higher Generalization Accuracy](https://mlsanity.com/paper/2302.10429/) (2023)
- [Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscape](https://mlsanity.com/paper/2305.11584/) (2023)
- [Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2204.10607/) (2022)
- [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)
- [RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates](https://mlsanity.com/paper/2207.12891/) (2022)
- [Locally Estimated Global Perturbations are Better than Local Perturbations for Federated Sharpness-aware Minimization](https://mlsanity.com/paper/2405.18890/) (2024)
- [FedADC: Accelerated Federated Learning with Drift Control](https://mlsanity.com/paper/2012.09102/) (2020)
- [FedADMM: A Robust Federated Deep Learning Framework with Adaptivity to System Heterogeneity](https://mlsanity.com/paper/2204.03529/) (2022)

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

- [First-Order Softmax Weighted Switching Gradient Method for Distributed Stochastic Minimax Optimization with Stochastic Constraints](https://mlsanity.com/paper/2603.05774/) (2026)
- [Rethinking the Personalized Relaxed Initialization in the Federated Learning: Consistency and Generalization](https://mlsanity.com/paper/2604.12768/) (2026)

## Abstract (arXiv)

As a popular paradigm for juggling data privacy and collaborative training, federated learning (FL) is flourishing to distributively process the large scale of heterogeneous datasets on edged clients. Due to bandwidth limitations and security considerations, it ingeniously splits the original problem into multiple subproblems to be solved in parallel, which empowers primal dual solutions to great application values in FL. In this paper, we review the recent development of classical federated primal dual methods and point out a serious common defect of such methods in non-convex scenarios, which we say is a "dual drift" caused by dual hysteresis of those longstanding inactive clients under partial participation training. To further address this problem, we propose a novel Aligned Federated Primal Dual (A-FedPD) method, which constructs virtual dual updates to align global consensus and local dual variables for those protracted unparticipated local clients. Meanwhile, we provide a comprehensive analysis of the optimization and generalization efficiency for the A-FedPD method on smooth non-convex objectives, which confirms its high efficiency and practicality. Extensive experiments are conducted on several classical FL setups to validate the effectiveness of our proposed method.