mlsanityData to 7 Oct 2026

Achieving Linear Speedup for Composite Federated Learning

arXiv 2602.03357 ↗First posted 3 Feb 2026cs.LG math.OCcited by 0

Not on the map. Why?

Abstract (arXiv)

This paper proposes FedNMap, a normal map-based method for composite federated learning, where the objective consists of a smooth loss and a possibly nonsmooth regularizer. FedNMap leverages a normal map-based update scheme to handle the nonsmooth term and incorporates a local correction strategy to mitigate the impact of data heterogeneity across clients. Under standard assumptions, including smooth local losses, weak convexity of the regularizer, and bounded stochastic gradient variance, FedNMap achieves linear speedup with respect to both the number of clients and the number of local updates for nonconvex losses, both with and without the Polyak-Lojasiewicz condition. To the best of our knowledge, this is the first algorithm establishing linear speedup for nonconvex composite federated learning. Numerical experiments corroborate our theoretical findings and demonstrate the linear speedup of FedNMap.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 32 references that are in the map. First posted on arXiv 3 Feb 2026.

Builds on

25 of 32 references.

References · 25

  1. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  2. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,592
  3. 2018Federated Optimization in Heterogeneous Networkscited by 2,971
  4. 2019Federated Learning: Challenges, Methods, and Future Directionscited by 1,531
  5. 2019On the Convergence of FedAvg on Non-IID Datacited by 1,220
  6. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
  7. 2018Stochastic model-based minimization of weakly convex functionscited by 157
  8. 2020Better Theory for SGD in the Nonconvex Worldcited by 156
  9. 2020FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Datacited by 143
  10. 2013Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimizationcited by 142
  11. 2016Distributed Mean Estimation with Limited Communicationcited by 134
  12. 2020Federated Composite Optimizationcited by 49
13 more
  1. 2019Stochastic Gradient Descent for Nonconvex Learning without Bounded Gradient Assumptionscited by 48
  2. 2022Fast Composite Optimization and Statistical Recovery in Federated Learningcited by 12
  3. 2023Composite federated learning with heterogeneous datacited by 7
  4. 2023A Normal Map-Based Proximal Stochastic Gradient Method: Convergence and Identification Propertiescited by 5
  5. 2024Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Datacited by 5
  6. 2021A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimizationcited by 4
  7. 2023Distributed Stochastic Optimization under a General Variance Conditioncited by 4
  8. 2023A New Random Reshuffling Method for Nonsmooth Nonconvex Finite-sum Optimizationcited by 4
  9. 2025A Proximal Operator for Inducing 2:4-Sparsitycited by 4
  10. 2025Non-convex composite federated learning with heterogeneous datacited by 4
  11. 2025FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Datacited by 4
  12. 2024Distributed Normal Map-based Stochastic Proximal Gradient Methods over Networkscited by 1
  13. 2025Composite Optimization with Error Feedback: the Dual Averaging Approachcited by 1

Built on by

Not cited yet.