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REVIEW 2 major objections 6 minor 25 references

Balancing Client Participation in Federated Learning Using AoI

T0 review · 2 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Age-of-information client selection makes federated learning converge faster and fairer.

desk verdict Plausible AoI scheduling idea, but the reported convergence gains are likely a weighting artifact and the theory does not cover the evaluated random-size policy. read the letter →

arxiv 2505.05099 v1 pith:IKZGZCXH submitted 2025-05-08 cs.LG cs.ITmath.IT

Alireza Javani , Zhiying Wang This is my paper · ORCID
classification cs.LGcs.ITmath.IT
keywords federatedlearningclientselectionageofinformationloadbalancingMarkovschedulingconvergenceanalysisnon-IIDdataFedAvg
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 claims that in federated learning, how evenly the server spaces out each client's turns matters as much as which clients get picked, and that age-of-information (AoI) scheduling can enforce even spacing with almost no central oversight. Instead of selecting clients uniformly at random each round, each client runs a small Markov chain on its own age (rounds since last update) and becomes more likely to be selected the older its update is; the optimal transition probabilities make the gaps between a client's selections nearly constant. The authors prove a convergence bound in which federated averaging's error depends on the variance of the aggregation weights, and they show that the AoI policy drives that variance down. In simulations on MNIST, CIFAR-10, and CIFAR-100, the optimal Markov policy reaches target accuracy in fewer rounds than random FedAvg selection, with reported gains of 7.5% and up to 20% in IID and non-IID settings. The reason a reader should care is that communication rounds are the bottleneck in federated learning, so a parameter-free rule that spreads participation evenly could make training faster and fairer without changing the learning algorithm.

What carries the argument

The engine of the method is a finite Markov chain whose states are a client's age a ∈ {0,1,...,m′}: in each round a client at age a is selected with probability p_a, resetting to state 0, or with probability 1−p_a advances to age a+1 (staying at m′ if already maximal). The load metric X is the peak age, and Theorem 1 gives the p_a that minimize Var[X] for a given selection rate m/n: a threshold schedule that keeps p_a = 0 until near the target interval and then selects almost surely, with a single fractional step when the target interval is not an integer. This Markov policy is what carries the argument: it turns the vague goal of 'balanced participation' into an explicit variance-minimization problem, it can be run by clients independently without the server tracking anyone, and its effect on learning is then visible in the convergence bound through Σ, the summed variance of the aggregation weights, and the selection skew ρ.

What would settle it

Run the identical experimental setup (100 clients, 15 per round, same datasets and optimizer) but replace the random baseline's data-size weighting with the same uniform aggregation weights used by the Markov policies. If random selection with uniform weights reaches the target accuracy as fast as the optimal Markov policy, then the central claim that AoI scheduling improves convergence is not supported. A second check: compare the optimal Markov policy against deterministic round-robin; if round-robin matches it, the benefit comes from low selection-interval variance, not from the Markov structure itself.

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Extended reading notes

Core claim

On its own terms, the central discovery is that client-selection load imbalance is a first-order cause of slow federated learning convergence, and that it can be removed by an age-based Markov policy. The paper defines the load metric X as the number of rounds between successive selections of a client, observes that X is the peak age from age-of-information theory, and formulates the goal as minimizing Var[X] subject to each client having the same per-round selection probability m/n. The optimal solution, carried over from the authors' earlier work, is a threshold policy: do not select a client until it reaches a fixed age, then select it with probability one at that age or with one fractional probability near the threshold. The theoretical contribution is Theorem 2, a convergence bound for federated averaging under biased selection in which the error contains a term proportional to Σ = sum_i Var[ω_i], the variance of the aggregation weights, and inversely related to the selection skew ρ. Because the Markov policy makes selection intervals nearly deterministic, it makes each client's long-run weight stable and markedly reduces Σ relative to random selection; the simulations show this translates into reaching the same accuracy in up to 20% fewer rounds, with steadier progress. The paper also computes closed-form Σ for random, data-size-proportional, and Markov policies (Theorems 3–5), so the variance reduction is quantified rather than asserted.

Load-bearing premise

The load-bearing premise is that the reported convergence speedup is caused by the age-based scheduling rule; but the experiments change the aggregation weighting scheme at the same time, so the gains may be partly or wholly due to using uniform weights rather than to the AoI policy.

Editorial extensions

If this is right

  • If the convergence bound is correct, any client selection policy reduces the error bound by shrinking Σ = sum_i Var[ω_i], so making selection intervals regular is not just a fairness nicety but a convergence accelerator.
  • The optimal Markov policy reaches the same target accuracy in fewer communication rounds than random FedAvg selection: e.g., 39 vs 45 rounds for 97% accuracy on IID MNIST, 95 vs 108 rounds for 75% accuracy on IID CIFAR-10, and up to 20% fewer on CIFAR-100 non-IID.
  • Because the policy is decentralized and depends only on each client's own age, it can be deployed with minimal server-side bookkeeping and no extra coordination messages.
  • The non-optimal increasing-p_a Markov policy also beats random selection but trails the optimal threshold, indicating that the variance-minimizing choice of p_a, not just age-aware selection, is what buys the speedup.

Reading between the lines

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

  • My reading: the headline comparison is not fully controlled. The random baseline uses data-size weighting during aggregation while the Markov policies use uniform weights, so part of the reported gain could come from removing weight variance rather than from age-based spacing; rerunning random selection with uniform weights would isolate the scheduling effect.
  • An extension the authors leave implicit: the same Markov-age machinery could be applied to client availability and energy budgets, where 'age' is replaced by time since a client's last participation and the threshold adapts to heterogeneous participation costs.
  • A testable prediction of their variance story: any policy that equalizes inter-selection intervals, such as deterministic round-robin, should produce convergence close to the optimal Markov policy on the same task, because it also drives Σ toward zero.
  • The convergence bound suggests selection skew ρ matters separately from Σ; a policy that biases selection toward high-loss clients could be combined with the age threshold to get the variance benefit and the skew benefit at once, which the paper does not explore.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper proposes an Age-of-Information-based client selection policy for federated learning. Clients are modeled by a Markov chain on their age, and age-dependent selection probabilities are chosen to minimize the variance of the inter-selection interval X. The authors prove a convergence bound (Theorem 2) showing that FL convergence depends on Sigma = sum_i Var[omega_i] and on selection skew rho, derive Sigma for random-with-data-size weighting, probabilistic data-size sampling, and Markov age-based policies (Theorems 3-5), and report image-classification experiments (MNIST, CIFAR-10, CIFAR-100) claiming 7.5-20% faster convergence for the optimal Markov policy over FedAvg/random selection.

Significance. If the claims are established, the paper offers a low-overhead decentralized selection rule and a clean theoretical link between aggregation-weight variance and FL convergence. The explicit variance formulas in Theorems 3-5, the convergence bound in Theorem 2, and the Markov construction are genuine strengths, and the optimality theorem is not circular because it is imported from the authors' prior work [27] rather than fitted to the simulation data. However, as submitted, the main empirical claim is not isolated: the baseline and the proposed policies differ in aggregation weights as well as in the selection rule, and the convergence theorem assumes a fixed number of selected clients while the evaluated Markov policy has a random batch size. These issues must be resolved before the contribution can be assessed.

major comments (2)
  1. [Section V (Figs. 5-7); Section III-B.1 and III-B.3; Theorem 2 and Remark 1] The comparison that supports the abstract's 7.5-20% speedup changes two variables at once. Policy 1 (Section III-B.1, Eq. (28)) weights each selected client by d_i / sum_{j in S} d_j, while Policies 3 and 4 (Section III-B.3, Theorem 5, Eq. (32)) weight uniformly as 1/|S|. Since Theorem 2 and Remark 1 identify Sigma = sum_i Var[omega_i] as the driver of convergence, the lower Sigma reported for the Markov policies (0.055 and 0.061 vs. 0.204 for Policy 1 in Figure 2) may be entirely due to the uniform weighting, not to age-based scheduling. In fact, by Theorem 3 and Remark 4, a random-selection baseline with uniform weights has Sigma = 1/m - 1/n = 1/15 - 1/100 = 0.0567 for n=100, m=15, essentially identical to the reported optimal Markov value of 0.055. A uniform-weight random-selection baseline must be run, and the convergence comparison repeated, before the AoI scheduling effect can be attributed to the selection policy.
  2. [Section IV, Eq. (11); Theorem 5; Lemmas 2-3] The convergence proof assumes that the number of selected clients is a constant m (Eq. (11)), but the evaluated Markov policy has random |S|, modeled in Theorem 5 as Binomial(n, p_avg). The bounds in Lemma 2 and Lemma 3 use the fixed quantity m (e.g., the factor 1/m in Eq. (38) and the m(Sigma+1) in Lemma 3), so Theorem 2 does not apply to Policy 3 as evaluated. The authors should either extend the convergence analysis to random |S| or evaluate a fixed-size version of the Markov policy whose m is constant.
minor comments (6)
  1. [Section V, Figure 2 caption] The notation is inconsistent: the Figure 2 caption uses k=15 for the number of selected clients and 'maximum client age of m=10', while the body uses m for the number of selected clients and m' for the maximum age; please align the notation throughout.
  2. [Section IV, Theorem 1] Theorem 1 is stated without proof and is the basis for the optimal Markov policy; state explicitly that it is proved in [27] and, if space permits, include a self-contained proof in the appendix.
  3. [Section IV, Theorem 2 proof] Reconcile the exponent of K in the variance term: Eqs. (72)-(73) give eta_t^2 m K^2 sigma^2, whereas the theorem statement in Eq. (27) has m K sigma^2; one of these is a typo.
  4. [Section IV, Definition 1 and Table II] The table reports rho as an 'average' over rounds, but Definition 1 uses minima and maxima over states, client subsets, and model parameters; clarify how the reported values are computed so the table can be reproduced.
  5. [Section V, Figures 5-7] The target accuracy thresholds differ across datasets (97% on MNIST, 75% on CIFAR-10, 30% on CIFAR-100), so the percentage speedups are not comparable across datasets unless this is explicitly stated.
  6. [Abstract and Section III-B.1] The abstract's phrase 'FedAvg selection approach' is imprecise: FedAvg is an aggregation algorithm, and the baseline is random client selection with data-size-proportional weights (Policy 1).

Circularity Check

1 steps flagged · score 6.0 of 10

AoI convergence gain collapses to uniform-weighting artifact per the paper's own Sigma formula.

  1. renaming known result [Section III-C (Theorem 5, Eq. 33) and Section IV (paragraph after Theorem 2)]
    "Then, the sum of the variances of the weights over all n clients is given by Sigma = sum_{s=1}^n (1/s) binom(n,s) (p_avg)^s (1-p_avg)^{n-s} - 1/n. ... On the other hand, AoI-based policies aim to minimize Sigma by selecting clients with fresher updates more frequently, thus ensuring that their influence on the global model remains stable and reducing the variability in the weights."

    Eq. (33) shows that the Markov policy's Sigma depends only on p_avg, the steady-state selection probability, and not on the age-dependent probabilities p_a that constitute the AoI scheduling mechanism. Under constraint (3), p_avg = m/n, so any Markov policy with uniform weights has the same Sigma as a uniform-weight random selection; Remark 4 gives Sigma = 1/m - 1/n for that random baseline, numerically about 0.0567 for n=100, m=15, essentially the paper's reported Markov-optimal 0.055. The convergence speedup is attributed via Theorem 2 to reduced Sigma, but the reduction is already achieved by switching from data-size weights (baseline Policy 1) to uniform weights.

full rationale

The paper's derivation is largely self-contained: Theorem 2 is proved in the appendix with assumptions following external works [25,26], and Theorems 3-5 compute Sigma directly. Theorem 1 is imported from the authors' prior work [27] as a parameter-free optimization result about the inter-selection interval, not about FL convergence, so that self-citation is not circular. The load-bearing circularity problem is the comparison in Section V: Policy 1 uses data-size weights while the Markov policies use uniform weights, and the paper's own Theorem 5 shows the Markov policy's Sigma depends only on p_avg, not on the AoI scheduling probabilities. Consequently, the convergence improvement claimed for the 'optimal Markov variant' reduces to the known variance reduction from uniform weighting, making the AoI-specific attribution circular rather than an independent empirical finding.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The proposed method introduces no new physical entities or fitted constants. The main theoretical reliance is on the authors' prior optimality theorem [27] and standard FL assumptions. The most consequential assumption is the fixed |S|=m in the convergence analysis, which conflicts with the random team size produced by the Markov policy.

free parameters (2)
  • maximum client age m' = 10 (in simulations)
    m' truncates the Markov state space and determines the optimal transition probabilities in Theorem 1; the paper sets m'=10 without sensitivity analysis.
  • non-optimal Markov transition probabilities p_a = unspecified
    The non-optimal variant is defined only by the ordering p0 < p1 < ... < pm'; the actual numeric values used in Figures 3-7 are not reported, so the schedule is an unspecified hand choice.
assumptions (4)
  • domain assumption Assumptions 1-4: L-smoothness, mu-strong convexity, unbiased stochastic gradients with bounded variance (sigma^2), and bounded expected squared gradient norm (G^2).
    These standard assumptions are invoked in Theorem 2 and its proof (Section IV and Appendix).
  • ad hoc to paper The number of selected clients is a constant m, stated as |S| = m in equation (11).
    This assumption is used in Theorem 2, but the proposed Markov policy selects each client independently, yielding a random |S| modeled as Binomial(n, pavg) in Theorem 5. The convergence proof therefore does not cover the proposed policy as specified.
  • domain assumption Client selections are independent across clients in steady state, so |S| follows a Binomial(n, pavg) distribution in Theorem 5.
    This independence is used in the proof of Theorem 5 to compute E[1/|S|].
  • domain assumption The load metric X has the same distribution for all clients.
    This symmetry assumption is stated in Section III-A before formulating the variance minimization problem (2).

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Cite this review

Pith. "Pith review of Balancing Client Participation in Federated Learning Using AoI." pith.science (2026). https://pith.science/paper/IKZGZCXH

@misc{pith2026250505099,
  author       = {Pith},
  title        = {Pith review of: Balancing Client Participation in Federated Learning Using AoI},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IKZGZCXH}},
  note         = {Machine review of arXiv:2505.05099}
}
abstract

Federated Learning (FL) offers a decentralized framework that preserves data privacy while enabling collaborative model training across distributed clients. However, FL faces significant challenges due to limited communication resources, statistical heterogeneity, and the need for balanced client participation. This paper proposes an Age of Information (AoI)-based client selection policy that addresses these challenges by minimizing load imbalance through controlled selection intervals. Our method employs a decentralized Markov scheduling policy, allowing clients to independently manage participation based on age-dependent selection probabilities, which balances client updates across training rounds with minimal central oversight. We provide a convergence proof for our method, demonstrating that it ensures stable and efficient model convergence. Specifically, we derive optimal parameters for the Markov selection model to achieve balanced and consistent client participation, highlighting the benefits of AoI in enhancing convergence stability. Through extensive simulations, we demonstrate that our AoI-based method, particularly the optimal Markov variant, improves convergence over the FedAvg selection approach across both IID and non-IID data settings by $7.5\%$ and up to $20\%$. Our findings underscore the effectiveness of AoI-based scheduling for scalable, fair, and efficient FL systems across diverse learning environments.

Figures

Figures reproduced from arXiv: 2505.05099 by the authors.

Figure 1
Figure 1. Markov chain with m′ + 1 states. enhancing fairness, but without guaranteeing optimal load balancing. C. Mathematical Analysis of Age-Based Client Selection In this section, we focus on a more detailed mathematical treatment of the age-based client selection policy introduced in Section 3. Specifically, we analyze the number of rounds it takes for a specific client to be selected in a Markov-based client selection s… view at source ↗
Figure 3
Figure 3. Empirical inter-selection interval distributions for four [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 2
Figure 2. Total Variance Σ over 1000 rounds. The simulation was performed with n = 100 clients, k = 15 selected clients per round, and a maximum client age of m = 10. The figure compares : Policy 1 (Random Weighted), Policy 2 (Probabilistic), Policy 3 (Markov Optimal), and Policy 4 (Markov Non-Optimal) [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Normalized variance √ Var(Y ) T versus window size T for four client selection policies: Random selection (Policy 1), Probabilistic (Policy 2), Markov Optimal (Policy 3), and Markov Non-Optimal (Policy 4). The setup involves 100 clients, 1000 rounds, and the selection …
Figure 5
Figure 5. Figure 5: Accuracy on MNIST dataset across different client [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Accuracy on CIFAR-10 dataset across different client selection policies: Random selection (Policy 1), Probabilistic (Policy 2), Markov Optimal (Policy 3), and Markov Non￾Optimal (Policy 4). The experiment was conducted with 100 clients, 15 clients selected per round, a…
Figure 7
Figure 7. Figure 7: Accuracy on CIFAR-100 dataset across different client selection policies: Random selection (Policy 1), Probabilistic (Policy 2), Markov Optimal (Policy 3), and Markov Non￾Optimal (Policy 4). The experiment was conducted with 100 clients, 15 clients selected per round, …

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