REVIEW 4 major objections 6 minor 1 cited by
Enhancing the Convergence of Federated Learning Aggregation Strategies with Limited Data
T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read This paper introduces FedAvgOpt, a server-side aggregation strategy that reweights each client's model each round by solving a small nonlinear optimization, and reports that it beats five classical aggregation strategies in mean accuracy…
desk verdict A plausible but statistically under-supported heuristic aggregation rule; the empirical ranking could easily be noise, though the method is honest and worth a careful revision, not a desk reject. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the per-round weight vector $\alpha \in \mathbb{R}^n$ obtained by minimizing the objective $$f(x) = \sum_{j=1}^n \frac{\|w_{\mathrm{FedAvg}} x - w_j\|^2}{\|w_{\mathrm{FedAvg}} x + w_j\|^2},$$ where $w_{\mathrm{FedAvg}}$ is the data-count-weighted average of the local model weights $w_j$ from the $n$ clients. The aggregated model then becomes $w_{\mathrm{FedAvgOpt}} = \frac{1}{\sum_i n_i} \sum_i n_i w_i \alpha_i$, so that $\alpha = (1,\ldots,1)$ reduces exactly to FedAvg. The server solves this unconstrained nonlinear problem with a standard derivative-free simplex method initialized at the all-ones vector, and the reweighted average is passed to clients as the next round's global model.
What would settle it
Run the same four-client, four-backbone protocol with five or more different random 20/80 split seeds and report whether FedAvgOpt still achieves the highest mean accuracy in every case; if any other strategy surpasses it on average, the claim that it is the most stable across all four backbones would fail. Alternatively, construct a non-i.i.d. split where FedAvgOpt underperforms FedAvg by a clear margin.
Extended reading notes
Core claim
The central claim is that FedAvgOpt, a server-side aggregation function that reweights client models each round by solving a small optimization problem, outperforms FedAvg, FedAvgM, FedMedian, FedOpt, and FedYogi in mean aggregated test accuracy over ten federated rounds, across all four base models studied. Concretely, Table II reports FedAvgOpt reaching 0.82209 mean accuracy with DenseNet121 versus 0.79740 for FedMedian, and 0.70999 versus 0.67959 with InceptionV3. The paper also reports that FedAvgOpt's per-round accuracy curves are more stable, with fewer sharp drops, and that in three of the four backbones it achieves the highest first-round accuracy, exceeding the others by more than ten percentage points.
Load-bearing premise
The paper assumes that minimizing the ad hoc ratio-sum objective f(x) yields aggregation weights that generalize better, without a theoretical analysis of why that objective relates to generalization; the experiments also rely on a single 20/80 stratified split per client, so the ranking could depend on that particular split.
Editorial extensions
If this is right
- Switching the server-side aggregator from FedAvg to FedAvgOpt improves mean accuracy over ten rounds for all four tested backbones in the studied i.i.d. setting, with gains of roughly three accuracy points for InceptionV3 and DenseNet121.
- FedAvgOpt requires no client-side modifications and no additional communication beyond the local model weights, so it can be dropped into existing federated learning pipelines.
- In three of the four backbones (VGG16, ResNet50V2, DenseNet121), FedAvgOpt achieves the highest first-round accuracy, indicating faster initial convergence.
- For an unstable base model such as InceptionV3, FedAvgOpt's per-round curve avoids the significant accuracy drops seen with FedAvg, FedAvgM, FedOpt, and FedYogi.
- The method is tested with only 20% of each client's data used for training, so the reported improvements appear specifically in the limited-data regime the paper targets.
Reading between the lines
- A natural extension is to test FedAvgOpt under non-i.i.d. client distributions, since the current experiments use an i.i.d. stratified split and the paper explicitly lists this as future work; the mechanism may behave differently when client data is heterogeneous.
- The proposed objective is an ad hoc ratio of distance terms without a theoretical convergence or generalization guarantee, so a plausible falsifying scenario is a data split or base model where the extra optimization actually degrades accuracy relative to plain FedAvg.
- Because the ranking rests on a single random 20/80 split per client with no repeated seeds, an editorial caveat is that the reported order of strategies could be partly an artifact of that particular split; repeated trials would be needed to confirm the ordering.
- The ratio structure resembles a normalized distance that may relate to cosine-style similarity between weight vectors, which could offer a bridge to theoretical analysis of FedAvgOpt as a form of robust mean estimation.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes FedAvgOpt, a server-side federated learning aggregation strategy that reweights each client's contributed model by a per-client scalar alpha. The alphas are obtained by minimizing a heuristic objective f(x) defined in Eq. (1) as the sum, over clients, of ratios of squared distances between a reweighted average model and each local model, using the Nelder-Mead method from the initial point x0 = 1. The method is evaluated on a brain MRI classification task with four clients, four pretrained CNN base models (VGG16, InceptionV3, ResNet50V2, DenseNet121), and five baseline aggregation strategies (FedAvg, FedAvgM, FedMedian, FedOpt, FedYogi), under a simulated limited-data setting with 20% of each client's data used for training. The paper reports mean aggregated test accuracy over ten federated rounds and concludes in Section VII that FedAvgOpt is the most stable aggregation strategy of the six analyzed across the four base models.
Significance. If the empirical claim were firmly established, FedAvgOpt would be a modest but potentially useful contribution: it is a server-side-only aggregation rule that requires no client-side modifications, which is practically attractive for privacy-sensitive medical deployments. The experimental design is transparent in several respects: it uses an open dataset, four architectures with very different parameter counts and depths, six aggregation strategies, and a clearly stated pseudocode for the proposed method. However, the central conclusion currently rests on a single experimental realization with no repeated seeds, no confidence intervals, and no significance testing, and the reported performance metric (mean accuracy over rounds) can favor a strategy that starts well in round 1 even if its final-round performance is not superior. The optimization objective is also introduced heuristically with no theoretical link to generalization or convergence. These issues are load-bearing because the paper's main contribution is its empirical ranking of aggregation strategies; the ranking may change under repeated runs or under a different evaluation metric.
major comments (4)
- [Section VI, Table II, Section VII] The central claim that FedAvgOpt is 'the most stable aggregation strategy' is not statistically supported. The experiments appear to use a single random stratified client partition and a single random 20/80 train/test split per client, with no repeated seeds, no confidence intervals, and no significance tests. For two of the four base models the reported margins over the best baseline are very small: VGG16 0.77010 vs. 0.76742 for FedAvgM (+0.27 percentage points) and ResNet50V2 0.79142 vs. 0.78652 for FedMedian (+0.49 percentage points). Training is stochastic and the data split is random, so these differences are within plausible run-to-run variation. The authors should repeat the entire protocol with multiple seeds and report mean and standard deviation (or confidence intervals) for each strategy and model, and ideally perform a paired significance test across seeds.
- [Section VI, Table II, Figure 4] The primary reported metric, 'mean aggregated accuracy obtained in the 10 rounds,' is not a standard measure of the quality of the final federated model. Averaging over rounds mixes early-round behavior with convergence behavior, and the paper itself notes that FedAvgOpt starts from a higher first-round accuracy for VGG16, DenseNet121, and ResNet50V2. A strategy that has a high initial accuracy but converges to the same or lower final accuracy can therefore look better under this metric. The authors should additionally report the final-round test accuracy and per-round learning curves with variability, or clearly justify why mean-over-rounds is the appropriate target metric for the claimed convergence improvement.
- [Section IV, Eqs. (1)-(2), Algorithm 1] The FedAvgOpt objective is ad hoc: there is no theoretical argument or prior evidence that minimizing the sum of ratios of squared distances between a reweighted average and each local model improves the global model's generalization or convergence. In addition, the alpha_i are optimized without any normalization or non-negativity constraint, so the resulting w_FedAvgOpt is not in general a convex combination of the client models; the paper does not discuss whether negative or large alpha values can occur or what effect they have on the aggregated model. The notation in Eq. (2), 'w_FedAvg x,' is also ambiguous: w_FedAvg appears to be a vector of aggregated parameters, while x is the alpha vector, so the expression should be written as the weighted average (1/sum n_i) * sum_i w_i n_i x_i rather than as a product of w_FedAvg and x. The authors should clarify the formulation, add constraints or justify their absence, and discuss the behavior of the Nelder-Mead optimization from the single starting point x0 = 1.
- [Section V, Section V.C] The local training configuration is incompletely specified: the paper gives the optimizer, learning rate, batch size, and number of rounds, but does not state the number of local training epochs (or local steps) per client per round. Local epochs are a critical hyperparameter in federated learning and directly affect the comparison between aggregation strategies. Without this information, the experiments are not fully reproducible, and the observed ranking could depend on an undocumented choice. The authors should report the number of local epochs/steps for each base model and, if varied, justify the choice.
minor comments (6)
- [Section I] There is a typo in the Introduction: 'psedudonymization' should be 'pseudonymization.'
- [Section VI] There are typos in the results discussion: 'mote than 10%' should be 'more than 10%,' and 'FedAvgOot' should be 'FedAvgOpt.'
- [Section V.B] In the ResNet-50 V2 description, '128 sy neurons' appears to be a typo for '128 neurons.'
- [Section IV, Eq. (2)] The notation 'w_FedAvg x' in Eq. (2) should be explicitly defined as the weighted average of client weights with coefficients x_i; as written, it looks like a matrix-vector product and is inconsistent with Eq. (1).
- [Section V.A] The paper should state the random seed or seeds used for the client partition and the train/test split, since the entire evaluation is based on a single split.
- [Section II] The descriptions of FedAvgM, FedMedian, and FedOpt would benefit from explicit references to the exact algorithm numbers and equations in the cited papers, since the current text summarizes rather than reproduces the update rules.
Circularity Check
No circularity: FedAvgOpt's alpha weights are optimized on client model weights, not on test labels, and the reported accuracy is an independent benchmark result.
full rationale
The FedAvgOpt construction (Section IV, Eqs. 1-2 and Algorithm 1) defines an optimization over the current round's client weights w_i, with the auxiliary objective f(x) measuring a reweighted average's distance to those same local models. The test-set accuracies in Table II are computed after aggregation on held-out client test data and never enter the objective or the Nelder-Mead optimization, so the method is not fitting test outcomes. The only self-citation, reference [10], is used to describe the standard federated learning architecture and is not load-bearing for the proposed strategy's validity or for the convergence comparison. The paper's empirical claim is a benchmark observation rather than a prediction derived from fitted constants, and there is no equation or prior result that forces FedAvgOpt's reported superiority by construction. Statistical concerns about one random split and small margins are robustness/correctness risks, not circularity.
Assumptions & free parameters
free parameters (2)
- alpha (per-client reweighting factors) =
not reported; optimized per round via Nelder-Mead
- Nelder-Mead initial point x0 =
1 (vector of ones)
assumptions (4)
- ad hoc to paper Minimizing f(x) (Eq. 1) improves the global model's convergence and accuracy
- domain assumption A single random stratified split into 4 i.i.d. clients with 20% training data is a sufficient testbed
- domain assumption ImageNet pre-training transfers to brain MRI
- domain assumption Nelder-Mead finds a meaningful minimum of f
Cite this review
Pith. "Pith review of Enhancing the Convergence of Federated Learning Aggregation Strategies with Limited Data." pith.science (2026). https://pith.science/paper/R4PW3A3R
@misc{pith2026250115949,
author = {Pith},
title = {Pith review of: Enhancing the Convergence of Federated Learning Aggregation Strategies with Limited Data},
year = {2026},
howpublished = {\url{https://pith.science/paper/R4PW3A3R}},
note = {Machine review of arXiv:2501.15949}
}
read the original abstract
The development of deep learning techniques is a leading field applied to cases in which medical data is used, particularly in cases of image diagnosis. This type of data has privacy and legal restrictions that in many cases prevent it from being processed from central servers. However, in this area collaboration between different research centers, in order to create models as robust as possible, trained with the largest quantity and diversity of data available, is a critical point to be taken into account. In this sense, the application of privacy aware distributed architectures, such as federated learning arises. When applying this type of architecture, the server aggregates the different local models trained with the data of each data owner to build a global model. This point is critical and therefore it is fundamental to analyze different ways of aggregation according to the use case, taking into account the distribution of the clients, the characteristics of the model, etc. In this paper we propose a novel aggregation strategy and we apply it to a use case of cerebral magnetic resonance image classification. In this use case the aggregation function proposed manages to improve the convergence obtained over the rounds of the federated learning process in relation to different aggregation strategies classically implemented and applied.
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