# FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Data

arXiv: https://arxiv.org/abs/2504.11903 · HTML: https://mlsanity.com/paper/2504.11903/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 56 references that are in the map.
- First posted on arXiv 16 Apr 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [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)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (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)
- [FedDC: Federated Learning with Non-IID Data via Local Drift Decoupling and Correction](https://mlsanity.com/paper/2203.11751/) (2022)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [Local Learning Matters: Rethinking Data Heterogeneity in Federated Learning](https://mlsanity.com/paper/2111.14213/) (2021)
- [Federated Learning for Generalization, Robustness, Fairness: A Survey and Benchmark](https://mlsanity.com/paper/2311.06750/) (2023)
- [FedVARP: Tackling the Variance Due to Partial Client Participation in Federated Learning](https://mlsanity.com/paper/2207.14130/) (2022)
- [Federated Composite Optimization](https://mlsanity.com/paper/2011.08474/) (2020)
- [Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2204.10607/) (2022)
- [Momentum Benefits Non-IID Federated Learning Simply and Provably](https://mlsanity.com/paper/2306.16504/) (2023)
- [FedADMM: A Federated Primal-Dual Algorithm Allowing Partial Participation](https://mlsanity.com/paper/2203.15104/) (2022)
- [A Simple Proximal Stochastic Gradient Method for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/1802.04477/) (2018)
- [FedDR -- Randomized Douglas-Rachford Splitting Algorithms for Nonconvex Federated Composite Optimization](https://mlsanity.com/paper/2103.03452/) (2021)
- [Accelerating Hybrid Federated Learning Convergence under Partial Participation](https://mlsanity.com/paper/2304.05397/) (2023)
- [Variable Smoothing for Weakly Convex Composite Functions](https://mlsanity.com/paper/2003.07612/) (2020)
- [Fast Composite Optimization and Statistical Recovery in Federated Learning](https://mlsanity.com/paper/2207.08204/) (2022)
- [A Stochastic Proximal Gradient Framework for Decentralized Non-Convex Composite Optimization: Topology-Independent Sample Complexity and Communication Efficiency](https://mlsanity.com/paper/2110.01594/) (2021)
- [Compressed Decentralized Proximal Stochastic Gradient Method for Nonconvex Composite Problems with Heterogeneous Data](https://mlsanity.com/paper/2302.14252/) (2023)
- [Proximal Stochastic Recursive Momentum Methods for Nonconvex Composite Decentralized Optimization](https://mlsanity.com/paper/2211.11954/) (2022)
- [Efficient Federated Learning against Heterogeneous and Non-stationary Client Unavailability](https://mlsanity.com/paper/2409.17446/) (2024)
- [Byzantine-Robust Distributed Online Learning: Taming Adversarial Participants in An Adversarial Environment](https://mlsanity.com/paper/2307.07980/) (2023)

## Built on by (most cited first, 4 of 4)

- [FedSLoP: Memory-Efficient Federated Learning with Low-Rank Gradient Projection](https://mlsanity.com/paper/2604.24012/) (2026)
- [Subspace Optimization for Efficient Federated Learning under Heterogeneous Data](https://mlsanity.com/paper/2604.25467/) (2026)
- [Achieving Linear Speedup for Composite Federated Learning](https://mlsanity.com/paper/2602.03357/) (2026)
- [Compressed Proximal Federated Learning for Non-Convex Composite Optimization on Heterogeneous Data](https://mlsanity.com/paper/2603.07654/) (2026)

## Abstract (arXiv)

Composite federated learning offers a general framework for solving machine learning problems with additional regularization terms. However, existing methods often face significant limitations: many require clients to perform computationally expensive proximal operations, and their performance is frequently vulnerable to data heterogeneity. To overcome these challenges, we propose a novel composite federated learning algorithm called FedCanon, designed to solve the optimization problems comprising a possibly non-convex loss function and a weakly convex, potentially non-smooth regularization term. By decoupling proximal mappings from local updates, FedCanon requires only a single proximal evaluation on the server per iteration, thereby reducing the overall proximal computation cost. Concurrently, it integrates control variables into local updates to mitigate the client drift arising from data heterogeneity. The entire architecture avoids the complex subproblems of primal-dual alternatives. The theoretical analysis provides the first rigorous convergence guarantees for this proximal-skipping framework in the general non-convex setting. It establishes that FedCanon achieves a sublinear convergence rate, and a linear rate under the Polyak-Lojasiewicz condition, without the restrictive bounded heterogeneity assumption. Extensive experiments demonstrate that FedCanon outperforms the state-of-the-art methods in terms of both accuracy and computational efficiency, particularly under heterogeneous data distributions.