Non-convex composite federated learning with heterogeneous data

Jiang Hu; Jiaojiao Zhang; Mikael Johansson

REVIEW 2 major objections 5 minor 35 references

Non-convex composite federated learning with heterogeneous data

T0 review · 2 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Sending the pre-proximal vector to the server recovers the true average gradient and removes client drift in composite federated learning.

desk verdict A solid non-convex composite FL paper with one repairable lemma inconsistency and an honest Bg residual; worth full peer review. read the letter →

arxiv 2502.03958 v1 pith:TPS2ZUUS submitted 2025-02-06 cs.LG cs.DC

Jiaojiao Zhang , Jiang Hu , Mikael Johansson This is my paper · ORCID

classification cs.LGcs.DC MSC 90C2690C1568W15

keywords non-convexcompositeoptimizationfederatedlearningheterogeneousdataclientdriftproximaloperatorlocalupdatesPolyak-Lojasiewiczinequalitycommunicationefficiency

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a federated algorithm for objectives of the form $F(x)=f(x)+g(x)$, where $f$ is smooth and possibly non-convex, averaged across clients, and $g$ is convex and non-smooth, such as an $\ell_1$ penalty. Each client runs $\tau$ local proximal-gradient steps while maintaining two quantities, a pre-proximal model and a post-proximal model, and transmits only the final pre-proximal model to the server. The paper claims that this decouples the proximal operation from communication: the transmitted vectors carry the average of the local gradients, so the server can mimic centralized proximal gradient descent without distortion, and a locally reconstructed correction term cancels client drift without extra communication. Under a global bound on the subgradients of $g$, it proves sublinear convergence to a bounded residual for general non-convex problems and linear convergence to a bounded residual when the composite objective satisfies the proximal Polyak–Łojasiewicz inequality. If the analysis holds, composite federated learning no longer has to choose between sparse regularizers, local updates, and low communication cost.

What carries the argument

The argument is carried by three linked devices. The first is the two-model bookkeeping: only the pre-proximal local model is transmitted, so the server sees the sum of gradients before the regularizer's proximal operator acts on them. The second is the correction term $c^{r+1}_i = \frac{1}{\eta_g\eta\tau}(P_{\tilde{\eta}}(x^r)-x^{r+1}) - \frac{1}{\tau}\sum_{t=0}^{\tau-1}\nabla f_i(z^r_{i,t};B^r_{i,t})$, which each client reconstructs from the broadcast global model; its average over clients is zero, which is exactly what keeps the transmitted average undistorted. The third is the auxiliary function $\Omega^r = F(P_{\tilde{\eta}}(x^r))-F^\star + \frac{1}{n\tilde{\eta}}\|\Lambda^r - \bar{\Lambda}^r\|^2$, whose first term tracks global suboptimality and whose second term bounds the local-drift error; Lemma A.1 and Lemma A.2 close the recursion on this drift term. The parameter $(t+1)\eta$ inside the local proximal operator is chosen so that the post-proximal local iterates approximate a centralized proximal gradient step on the global model, which is what makes the drift bound small enough to close.

What would settle it

A direct calculation settles the internal consistency: the proof of Lemma A.1 invokes $8(t+1)\eta^2 L^2 \leq 1/(8\tau)$, which requires $\tilde{\eta} \leq \eta_g/(8L)$, stricter than the lemma's stated $\tilde{\eta}\leq \eta_g/\sqrt{20L}$; the theorem's condition (13) with $\eta_g\ge 1.5$ and $\tilde{\eta}\le 1/(10L)$ implies the stricter bound, so the main theorems survive but the lemma statement is imprecise. Separately, run Algorithm 1 with full local gradients on a non-convex composite problem where $g$ is the indicator function of a box, so Assumption 3.1 fails and $B_g=\infty$, and check whether $\|G(P_{\tilde{\eta}}(x^r))\|^2$ goes to machine zero; exact convergence would show the $B_g$ residual is an artifact of the proof.

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Extended reading notes

Core claim

The load-bearing claim is that each client keeps two local models at every step, the pre-proximal variable $\hat{z}^r_{i,t}$ and the post-proximal variable $z^r_{i,t}=P_{(t+1)\eta}(\hat{z}^r_{i,t})$, evaluates stochastic gradients at the post-proximal model, and after $\tau$ updates sends only $\hat{z}^r_{i,\tau}$ to the server. Because the drift-correction terms $c^r_i$ average to zero across clients, the server's update becomes $x^{r+1}=P_{\tilde{\eta}}(x^r)-\tilde{\eta}\,\frac{1}{n\tau}\sum_{t=0}^{\tau-1}\sum_{i=1}^n\nabla f_i(z^r_{i,t};B^r_{i,t})$, which is a centralized proximal gradient step affected only by stochastic sampling, with no distortion from the nonlinear proximal map. This is the decoupling: the server can run a proximal step on the global model using the true average local gradient. The convergence analysis measures progress with the gradient mapping $G(P_{\tilde{\eta}}(x^r))=\frac{1}{\tilde{\eta}}(P_{\tilde{\eta}}(x^r)-\tilde{x}^{r+1})\in \nabla f(P_{\tilde{\eta}}(x^r))+\partial g(\tilde{x}^{r+1})$, and proves $\frac{1}{R}\sum_{r=1}^R \mathbb{E}\|G(P_{\tilde{\eta}}(x^r))\|^2 \leq \frac{\mathbb{E}[\Omega^1]}{0.3\tilde{\eta}R} + \frac{20\sigma^2}{n\tau b} + \frac{187L^2\tilde{\eta}^2 B_g^2}{\eta_g^2}$ for general non-convex problems, and $\mathbb{E}[\Omega^{R+1}] \leq (1-\frac{\mu\tilde{\eta}}{3})^R \mathbb{E}[\Omega^1] + \frac{18\sigma^2}{\mu n\tau b} + \frac{168L^2\tilde{\eta}^2 B_g^2}{\mu\eta_g^2}$ under the proximal PL inequality. These are stated as Theorem 3.5 and Theorem 3.6, with residuals set by stochastic variance and by the squared subgradient bound of the regularizer.

Load-bearing premise

The regularizer $g$ must have globally bounded subgradients (norm at most $B_g$), which fails for constraint-set indicator functions and makes the stated residual error infinite.

Editorial extensions

If this is right

A single $d$-dimensional vector per client per communication round is enough to remove client drift for non-convex composite objectives; the correction term is reconstructed locally from the broadcast global model, so no control-variate communication is needed.
Communication frequency can be reduced through local updates while the method keeps a per-round convergence guarantee; the variance term $\sigma^2/(n\tau b)$ shrinks with larger mini-batches and vanishes when full local gradients are used.
Under the proximal PL inequality the composite loss converges linearly to a neighborhood whose radius is set by the stochastic variance and by $B_g^2$, the squared subgradient bound of the regularizer.
If the regularizer has unbounded subgradients, such as an indicator function of a constraint set, the stated residual bounds are vacuous; the paper explicitly notes in Remark 3.7 that it cannot remove the $B_g$ term in the non-convex case.
Full-gradient experiments on sparse logistic regression show exact convergence with no visible $B_g$ residual, suggesting that the theoretical residual is conservative rather than a fundamental obstruction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The pre-proximal transmission idea may extend to other nonlinear client-side maps, such as variance-reduced proximal operators or adaptive-regularizer steps, whenever the server needs the average of a pre-image rather than a post-image.
The $B_g^2$ residual likely comes from the two-sided subgradient bound used in Lemma A.1; a drift bound that exploits one-sided or structure-dependent properties of $g$ could remove or shrink it for specific regularizers.
The proof of Lemma A.1 requires the stricter condition $\tilde{\eta} \leq \eta_g/(8L)$ at the step where it uses $8(t+1)\eta^2 L^2 \leq 1/(8\tau)$, while the lemma states only $\tilde{\eta} \leq \eta_g/\sqrt{20L}$; the theorem's global condition (13) appears to imply the stricter bound when $\eta_g\ge 1.5$, so the main theorems survive, but the lemma as written is imprecise.
Because the correction term uses the previous round's global gradient information, the drift correction is inherently one round stale; a testable variant with momentum or variance reduction over older gradients could shrink the residual at no extra communication cost.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a solid theory paper with a real algorithmic idea, and the main convergence claims survive scrutiny. The authors decouple proximal evaluation from communication by having clients send the pre-proximal model to the server, so the server can recover average gradients without the nonlinear distortion of the proximal map. They add a correction term built from the broadcast global model to cancel client drift while exchanging only one d-dimensional vector per client per round. That design is genuinely useful for sparse and regularized federated training. Relative to FedDR, FedADMM, FedDA, and Fast-FedDA, the non-convex and proximal-PL analyses for this decoupled local-update scheme are new; the strongly convex case appeared in their earlier ICASSP paper, and they cite it. The appendix gives a full Lyapunov proof with explicit lemmas and constants. Credit where it is earned: this is a substantive, reproducible theoretical contribution.

Soft spots, in proportion. Assumption 3.1 requires a uniform bound on subgradients of the regularizer. That covers l1 and ReLU but fails for indicator functions of constraint sets, so the main theorems give no guarantee in a canonical composite setting. The residual error in Theorems 3.5 and 3.6 scales with Bg^2, and the authors explicitly say they cannot remove it in the non-convex case. That is an honest scope restriction, not a fatal flaw. Second, Lemma A.1 states step-size tilde eta <= eta_g / sqrt(20 L), but the proof at (A.20) needs tilde eta <= eta_g / (8 L). The theorem's global condition (13) implies the stricter bound, so the main results are unaffected; the lemma as written is imprecise and should be fixed. Third, the numerical section is thin: no error bars, no FedDR/FedADMM baselines, no code. The experiments show the algorithm works and that the Bg residual does not show up in practice, but the word 'superiority' overstates the evidence.

The citation pattern looks fair: they position themselves against FedDA, Fast-FedDA, FedDR, FedADMM, and their own conference paper. The math is not machine-checked, and I did not verify every inequality, but the structure of the proof is coherent and the claimed rates match the method.

Who is this for: researchers working on communication-efficient composite federated learning with non-smooth regularizers. The proof machinery and the decoupling trick are worth studying. My recommendation: yes, send this to peer review. It deserves a serious referee. Require fixing Lemma A.1's condition, tightening the empirical claims, and adding at least one constraint-set experiment to confront the Bg limitation.

Referee Report

2 major / 5 minor

Summary. The paper addresses the composite federated learning problem (1) with a non-convex smooth loss f and a convex, possibly non-smooth regularizer g. It proposes Algorithm 1, in which each client maintains both a pre-proximal and a post-proximal local model, performs τ local updates using mini-batch stochastic gradients plus a client-drift correction term, and transmits only the pre-proximal model to the server. The server then updates a pre-proximal global model so that the server-side recursion mimics centralized proximal gradient descent. Under Assumptions 3.1–3.4 and step-size condition (13), the paper proves an average bound on the gradient mapping norm for general non-convex f (Theorem 3.5) and a linear convergence bound for the function value under the proximal PL inequality (Theorem 3.6), both with explicit residual errors depending on the stochastic variance and on the subgradient bound Bg. Numerical experiments on sparse logistic regression and CNN training on MNIST support the algorithmic claims.

Significance. If the results hold, Algorithm 1 is a meaningful step for composite federated learning: it decouples proximal evaluation from communication, requires only one d-dimensional vector per client per communication round, does not assume bounded data heterogeneity, and handles non-smooth regularizers. The convergence analysis is non-trivial and the appendix contains a full Lyapunov-style proof with explicit lemmas. The paper is also candid about its limitations, notably the residual term depending on Bg. The main concerns are a step-size condition mismatch in the appendix and the restrictive bounded-subgradient assumption on g; both are local and fixable, and the central algorithmic idea appears sound.

major comments (2)

[Appendix A.4, Lemma A.1 and Lemma A.2] Lemma A.1 is stated under the condition η̃ ≤ ηg/√(20L), but the proof of (A.20) uses the inequality 8(t+1)η²L² ≤ 1/(8τ), which is equivalent to η̃ ≤ ηg/(8L). For typical values of L this is a stricter condition than the one stated, so the lemma as written is not fully proven. Lemma A.2 has the same issue and also contains a typographical garble in its stated condition ("η̃ ≤ ηg√(20L)"). The step-size condition (13) in Theorems 3.5 and 3.6 does imply the stricter bound, so the main results are not invalidated, but the lemma statements must be corrected and Lemma A.2's hypothesis should match the proof requirements.
[Assumption 3.1 and Theorems 3.5–3.6] Assumption 3.1 requires the subgradient of g to be uniformly bounded by Bg. For many canonical composite problems, g is the indicator function of a convex constraint set, for which subgradients on the boundary are unbounded, making Bg infinite and the residual terms 187L²η̃²Bg²/ηg² (Theorem 3.5) and 168L²η̃²Bg²/(μηg²) (Theorem 3.6) vacuous. The authors acknowledge this limitation in Remark 3.7 and the conclusion, but the abstract and introduction present the result as a general treatment of non-convex composite FL. I recommend adding an explicit qualification in the abstract and a short discussion of settings where Bg is finite (e.g., ℓ1, ℓ∞, ReLU) and of possible avenues for removing the Bg residual under additional assumptions.

minor comments (5)

[Equation (2) and Appendix A.1] In the compact form (2), the two sums in the correction term are typeset identically, although one is the averaged gradient across clients and the other is the per-client gradient; please add the overbar or a textual clarification to avoid confusion.
[Section 4.2] The text reads "The remaining 3,0000 samples" and should be "The remaining 30,000 samples".
[Appendix A.4, Lemma A.2] The stated condition in Lemma A.2 appears as "η̃ ≤ ηg√(20L)" but should presumably be "η̃ ≤ ηg/√(20L)", and in any case must be updated to the stricter condition used in the proof.
[Notation and introduction] The phrase "sends only a single d-dimensional vector per communication round" is not fully precise because the server also broadcasts a d-dimensional vector; the per-client communication cost is correct, but the wording in the abstract could be clarified.
[Reference [22]] The proof of Lemma A.1 cites "[22, Corollary C.1]" for an inequality on the variance of averaged stochastic gradients; please verify that the cited result indeed appears in reference [22] and that the reference is complete.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the non-convex and proximal-PL convergence guarantees are derived from explicitly stated assumptions via a Lyapunov argument, and the only self-citation ([33]) is used for a separate strongly-convex theorem, not for the paper's central claims.

full rationale

The paper's central results, Theorems 3.5 and 3.6, are derived from Assumptions 3.1-3.4 using a constructed auxiliary function Omega^r, the drift bound in Lemma A.1, the recursion in Lemma A.2, and the server-side descent inequality based on Fact 1. None of these steps assumes the conclusion: the residual terms O(sigma^2/(n*tau*b)) and O(L^2*eta_tilde^2*B_g^2/eta_g^2) arise algebraically from the stochastic variance bound and from the bounded-subgradient constant B_g in Assumption 3.1, not from fitting any parameter to the output. The algorithm and the strongly-convex theorem from the authors' conference paper [33] are cited in Remark 3.7, but that citation is not load-bearing for the non-convex or proximal-PL proofs; those proofs are self-contained once the stated assumptions are accepted. The paper explicitly acknowledges that the (t+1)eta parameter choice is heuristic and that the B_g-dependent residual cannot be eliminated in the non-convex case; these are honest limitations, not circular reductions. The apparent mismatch in Lemma A.1 between the stated step-size condition and the stricter condition used inside its proof is a proof-technical imprecision, not a case of defining a prediction in terms of the input. Overall, the derivation chain is self-contained and the claims are not forced by definition or by self-citation.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The theoretical claims depend on four domain assumptions (bounded subgradient of g, L-smoothness, general non-convexity or proximal PL, and bounded stochastic gradient variance) plus standard proximal inequalities. No free parameters are fitted to obtain the rates; the step-size conditions in (13) are user choices, and the experimental hyperparameters are hand-tuned but do not affect the proof. No invented entities are introduced.

assumptions (5)

domain assumption The subgradient of the convex regularizer g is uniformly bounded: ∥∇g(x)∥ ≤ Bg for all x.
Assumption 3.1. Used throughout Lemmas A.1 and A.2 and in the residual terms of Theorems 3.5 and 3.6; fails for constraint-set indicators, making the bound vacuous.
domain assumption Each client loss fi is L-smooth.
Assumption 3.2. Used to bound gradient differences in the drift analysis and server update.
domain assumption The loss is either generally non-convex or satisfies the proximal PL inequality (3.3).
Assumption 3.3. Determines whether Theorem 3.5 or 3.6 applies; the proximal PL condition is an extra structural assumption for the linear rate.
domain assumption Local mini-batch gradients are unbiased with variance bounded by σ²/b.
Assumption 3.4. Controls the residual term O(σ²/(nτb)); standard in stochastic FL analysis.
standard math Proximal inequality Fact 1 from Reddi et al. [10] and nonexpansiveness of proximal maps.
Used in Appendix A.5 to derive the descent of the server-side update and in Lemma A.1 to bound the drift.

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Cite this review

Pith. "Pith review of Non-convex composite federated learning with heterogeneous data." pith.science (2026). https://pith.science/paper/TPS2ZUUS

@misc{pith2026250203958,
  author       = {Pith},
  title        = {Pith review of: Non-convex composite federated learning with heterogeneous data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TPS2ZUUS}},
  note         = {Machine review of arXiv:2502.03958}
}

read the original abstract

We propose an innovative algorithm for non-convex composite federated learning that decouples the proximal operator evaluation and the communication between server and clients. Moreover, each client uses local updates to communicate less frequently with the server, sends only a single d-dimensional vector per communication round, and overcomes issues with client drift. In the analysis, challenges arise from the use of decoupling strategies and local updates in the algorithm, as well as from the non-convex and non-smooth nature of the problem. We establish sublinear and linear convergence to a bounded residual error under general non-convexity and the proximal Polyak-Lojasiewicz inequality, respectively. In the numerical experiments, we demonstrate the superiority of our algorithm over state-of-the-art methods on both synthetic and real datasets.

Figures

Figures reproduced from arXiv: 2502.03958 by the authors.

**Figure 1.** Block diagram of Algorithm 1. 2.2 The intuition behind the algorithm design As shown in Appendix A.1, the iterates generated by 3 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Sparse logistic regression using full gradients with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 4.** Classification of MNIST using CNN with τ = 5 and τ = 10 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

Figures from the paper (1 more)

**Figure 3.** Figure 3: Sparse logistic regression using stochastic gradients [PITH_FULL_IMAGE:figures/full_fig_p008_3.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

35 extracted references · 30 canonical work pages

[1]

Privacy-preserving and communication-efficient energy prediction scheme based on federated learning for smart grids

Mahmoud M Badr, Mohamed Mahmoud, Yuguang Fang, Mohammed Abdulaal, Abdulah J Aljohani, Waleed Alasmary, and Mohamed I Ibrahem. Privacy-preserving and communication-efficient energy prediction scheme based on federated learning for smart grids. IEEE Internet of Things Journal, 10(9):7719–7736, 2023

work page 2023
[2]

Fast composite optimization and statistical recovery in federated learning

Yajie Bao, Michael Crawshaw, Shan Luo, and Mingrui Liu. Fast composite optimization and statistical recovery in federated learning. In International Conference on Machine Learning, pages 1508–1536, 2022. 14

work page 2022
[3]

A fast iterative shrinkage- thresholding algorithm for linear inverse problems

Amir Beck and Marc Teboulle. A fast iterative shrinkage- thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences , 2(1):183–202, 2009

2009
[4]

Online optimization of switched LTI systems using continuous-time and hybrid accelerated gradient flows

Gianluca Bianchin, Jorge I Poveda, and Emiliano Dall’Anese. Online optimization of switched LTI systems using continuous-time and hybrid accelerated gradient flows. Automatica, 146:110579, 2022

work page 2022
[5]

Sparse linear regression from perturbed data

Sophie M Fosson, Vito Cerone, and Diego Regruto. Sparse linear regression from perturbed data. Automatica, 122:109284, 2020

work page 2020
[6]

Distributed networked real-time learning

Alfredo Garcia, Luochao Wang, Jeff Huang, and Lingzhou Hong. Distributed networked real-time learning. IEEE Transactions on Control of Network Systems , 8(1):28–38, 2020

work page 2020
[7]

Mini- batch stochastic approximation methods for nonconvex stochastic composite optimization

Saeed Ghadimi, Guanghui Lan, and Hongchao Zhang. Mini- batch stochastic approximation methods for nonconvex stochastic composite optimization. Mathematical Programming, 155(1):267–305, 2016

2016
[8]

A strictly contractive Peaceman–Rachford splitting method for convex programming

Bingsheng He, Han Liu, Zhaoran Wang, and Xiaoming Yuan. A strictly contractive Peaceman–Rachford splitting method for convex programming. SIAM Journal on Optimization , 24(3):1011–1040, 2014

work page 2014

Show all 35 references

[9]

Distributed networked learning with correlated data

Lingzhou Hong, Alfredo Garcia, and Ceyhun Eksin. Distributed networked learning with correlated data. Automatica, 137:110134, 2022

2022
[10]

Proximal stochastic methods for nonsmooth nonconvex finite-sum optimization

Sashank J Reddi, Suvrit Sra, Barnabas Poczos, and Alexander J Smola. Proximal stochastic methods for nonsmooth nonconvex finite-sum optimization. Advances in Neural Information Processing Systems , 29, 2016

2016
[11]

Linear convergence of gradient and proximal-gradient methods under the Polyak- Lojasiewicz condition

Hamed Karimi, Julie Nutini, and Mark Schmidt. Linear convergence of gradient and proximal-gradient methods under the Polyak- Lojasiewicz condition. In Machine Learning and Knowledge Discovery in Databases, pages 795– 811, 2016

2016
[12]

Mime: Mimicking centralized stochastic algorithms in federated learning

Sai Praneeth Karimireddy, Martin Jaggi, Satyen Kale, Mehryar Mohri, Sashank J Reddi, Sebastian U Stich, and Ananda Theertha Suresh. Mime: Mimicking centralized stochastic algorithms in federated learning. arXiv preprint arXiv:2008.03606, 2020

2008 arXiv
[13]

Scaffold: Stochastic controlled averaging for federated learning

Sai Praneeth Karimireddy, Satyen Kale, Mehryar Mohri, Sashank Reddi, Sebastian Stich, and Ananda Theertha Suresh. Scaffold: Stochastic controlled averaging for federated learning. In International Conference on Machine Learning, pages 5132–5143, 2020

2020
[14]

Understanding notions of stationarity in nonsmooth optimization: A guided tour of various constructions of subdifferential for nonsmooth functions

Jiajin Li, Anthony Man-Cho So, and Wing-Kin Ma. Understanding notions of stationarity in nonsmooth optimization: A guided tour of various constructions of subdifferential for nonsmooth functions. IEEE Signal Processing Magazine, 37(5):18–31, 2020

2020
[15]

Federated optimization in heterogeneous networks

Tian Li, Anit Kumar Sahu, Manzil Zaheer, Maziar Sanjabi, Ameet Talwalkar, and Virginia Smith. Federated optimization in heterogeneous networks. Proceedings of Machine Learning and Systems , 2:429–450, 2020

2020
[16]

On the convergence of FedAvg on non-iid data

Xiang Li, Kaixuan Huang, Wenhao Yang, Shusen Wang, and Zhihua Zhang. On the convergence of FedAvg on non-iid data. In International Conference on Learning Representations, 2019

2019
[17]

Private non-convex federated learning without a trusted server

Andrew Lowy, Ali Ghafelebashi, and Meisam Razaviyayn. Private non-convex federated learning without a trusted server. In International Conference on Artificial Intelligence and Statistics , pages 5749–5786, 2023

2023
[18]

Error bounds and convergence analysis of feasible descent methods: a general approach

Zhi-Quan Luo and Paul Tseng. Error bounds and convergence analysis of feasible descent methods: a general approach. Annals of Operations Research , 46(1):157–178, 1993

1993
[19]

Communication- efficient learning of deep networks from decentralized data

Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication- efficient learning of deep networks from decentralized data. In Artificial Intelligence and Statistics , pages 1273–1282, 2017

2017
[20]

Gradient free cooperative seeking of a moving source

Elad Michael, Chris Manzie, Tony A Wood, Daniel Zelazo, and Iman Shames. Gradient free cooperative seeking of a moving source. Automatica, 152:110948, 2023

2023
[21]

Primal-dual subgradient methods for convex problems

Yurii Nesterov. Primal-dual subgradient methods for convex problems. Mathematical Programming, 120(1):221–259, 2009

2009
[22]

Differentially private federated learning on heterogeneous data

Maxence Noble, Aur´ elien Bellet, and Aymeric Dieuleveut. Differentially private federated learning on heterogeneous data. In International Conference on Artificial Intelligence and Statistics , pages 10110–10145, 2022

2022
[23]

FedSplit: An algorithmic framework for fast federated optimization

Reese Pathak and Martin J Wainwright. FedSplit: An algorithmic framework for fast federated optimization. Advances in Neural Information Processing Systems , 33:7057–7066, 2020

2020
[24]

Local SGD converges fast and communicates little

Sebastian U Stich. Local SGD converges fast and communicates little. In International Conference on Learning Representations, 2018

2018
[25]

FedDR–randomized Douglas-Rachford splitting algorithms for nonconvex federated composite optimization

Quoc Tran Dinh, Nhan H Pham, Dzung Phan, and Lam Nguyen. FedDR–randomized Douglas-Rachford splitting algorithms for nonconvex federated composite optimization. Advances in Neural Information Processing Systems , 34:30326–30338, 2021

2021
[26]

FedADMM: A federated primal-dual algorithm allowing partial participation

Han Wang, Siddartha Marella, and James Anderson. FedADMM: A federated primal-dual algorithm allowing partial participation. In 2022 IEEE 61st Conference on Decision and Control (CDC) , pages 287–294, 2022

2022
[27]

Decentralized nonconvex optimization with guaranteed privacy and accuracy

Yongqiang Wang and Tamer Ba¸ sar. Decentralized nonconvex optimization with guaranteed privacy and accuracy. Automatica, 150:110858, 2023

2023
[28]

On stochastic gradient and subgradient methods with adaptive steplength sequences

Farzad Yousefian, Angelia Nedi´ c, and Uday V Shanbhag. On stochastic gradient and subgradient methods with adaptive steplength sequences. Automatica, 48(1):56–67, 2012

2012
[29]

Federated composite optimization

Honglin Yuan, Manzil Zaheer, and Sashank Reddi. Federated composite optimization. In International Conference on Machine Learning, pages 12253–12266, 2021

2021
[30]

On convergence of FedProx: Local dissimilarity invariant bounds, non-smoothness and beyond

Xiaotong Yuan and Ping Li. On convergence of FedProx: Local dissimilarity invariant bounds, non-smoothness and beyond. Advances in Neural Information Processing Systems, 35:10752–10765, 2022

2022
[31]

A family of inexact SQA methods for non-smooth convex minimization with provable convergence guarantees based on the Luo–Tseng error bound property

Man-Chung Yue, Zirui Zhou, and Anthony Man-Cho So. A family of inexact SQA methods for non-smooth convex minimization with provable convergence guarantees based on the Luo–Tseng error bound property. Mathematical Programming, 174(1):327–358, 2019

2019
[32]

Secure and decentralized federated learning framework with non-iid data based on blockchain

Feng Zhang, Yongjing Zhang, Shan Ji, and Zhaoyang Han. Secure and decentralized federated learning framework with non-iid data based on blockchain. Heliyon, 10(5), 2024

2024
[33]

Composite federated learning with heterogeneous data

Jiaojiao Zhang, Jiang Hu, and Mikael Johansson. Composite federated learning with heterogeneous data. arXiv preprint arXiv:2309.01795, 2023

2023 arXiv
[34]

Fedaudio: A federated learning benchmark for audio tasks

Tuo Zhang, Tiantian Feng, Samiul Alam, Sunwoo Lee, Mi Zhang, Shrikanth S Narayanan, and Salman Avestimehr. Fedaudio: A federated learning benchmark for audio tasks. In IEEE International Conference on Acoustics, Speech and Signal Processing, pages 1–5, 2023

2023
[35]

FedPD: A federated learning framework with adaptivity to non-iid data

Xinwei Zhang, Mingyi Hong, Sairaj Dhople, Wotao Yin, and Yang Liu. FedPD: A federated learning framework with adaptivity to non-iid data. IEEE Transactions on Signal Processing, 69:6055–6070, 2021. 15

2021

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

Privacy-preserving and communication-efficient energy prediction scheme based on federated learning for smart grids

Mahmoud M Badr, Mohamed Mahmoud, Yuguang Fang, Mohammed Abdulaal, Abdulah J Aljohani, Waleed Alasmary, and Mohamed I Ibrahem. Privacy-preserving and communication-efficient energy prediction scheme based on federated learning for smart grids. IEEE Internet of Things Journal, 10(9):7719–7736, 2023

work page 2023

[2] [2]

Fast composite optimization and statistical recovery in federated learning

Yajie Bao, Michael Crawshaw, Shan Luo, and Mingrui Liu. Fast composite optimization and statistical recovery in federated learning. In International Conference on Machine Learning, pages 1508–1536, 2022. 14

work page 2022

[3] [3]

A fast iterative shrinkage- thresholding algorithm for linear inverse problems

Amir Beck and Marc Teboulle. A fast iterative shrinkage- thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences , 2(1):183–202, 2009

2009

[4] [4]

Online optimization of switched LTI systems using continuous-time and hybrid accelerated gradient flows

Gianluca Bianchin, Jorge I Poveda, and Emiliano Dall’Anese. Online optimization of switched LTI systems using continuous-time and hybrid accelerated gradient flows. Automatica, 146:110579, 2022

work page 2022

[5] [5]

Sparse linear regression from perturbed data

Sophie M Fosson, Vito Cerone, and Diego Regruto. Sparse linear regression from perturbed data. Automatica, 122:109284, 2020

work page 2020

[6] [6]

Distributed networked real-time learning

Alfredo Garcia, Luochao Wang, Jeff Huang, and Lingzhou Hong. Distributed networked real-time learning. IEEE Transactions on Control of Network Systems , 8(1):28–38, 2020

work page 2020

[7] [7]

Mini- batch stochastic approximation methods for nonconvex stochastic composite optimization

Saeed Ghadimi, Guanghui Lan, and Hongchao Zhang. Mini- batch stochastic approximation methods for nonconvex stochastic composite optimization. Mathematical Programming, 155(1):267–305, 2016

2016

[8] [8]

A strictly contractive Peaceman–Rachford splitting method for convex programming

Bingsheng He, Han Liu, Zhaoran Wang, and Xiaoming Yuan. A strictly contractive Peaceman–Rachford splitting method for convex programming. SIAM Journal on Optimization , 24(3):1011–1040, 2014

work page 2014