BEFL: Balancing Energy Consumption in Federated Learning for Mobile Edge IoT

Fuke Shen; Tongquan Wei; Zehao Ju

REVIEW 4 major objections 4 minor 25 references

BEFL: Balancing Energy Consumption in Federated Learning for Mobile Edge IoT

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read BEFL cuts federated-learning energy variance by 72.7% while improving accuracy.

desk verdict Useful incremental idea for energy-balanced FL client selection, but the headline energy savings are computed with a self-referential synthetic metric that needs hardware validation before I'd trust the 72.7%. read the letter →

arxiv 2412.03950 v1 pith:JGTEQABE submitted 2024-12-05 cs.LG cs.DC

Zehao Ju , Tongquan Wei , Fuke Shen This is my paper · ORCID

classification cs.LGcs.DC

keywords federatedlearningenergyconsumptionclientselectionreinforcementimitationresourceallocationmobileedgeIoTfairness

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 argues that energy imbalance among devices, not just total energy use, is what hurts federated learning on battery-powered mobile IoT devices. It proposes BEFL, a joint optimization framework that allocates communication resources with the SLSQP algorithm and selects clients through a heuristic that clusters devices by ideal energy consumption, then uses that heuristic to pre-train a reinforcement learning agent. In simulations on CIFAR-10 and MNIST, BEFL improves global model accuracy by about 1.6%, cuts variance in device energy consumption by up to 72.7%, and lowers total energy consumption by 28.2% relative to existing methods. The significance is that federated learning deployments on energy-sensitive devices could last longer and lose fewer participants if energy fairness is made an explicit objective.

What carries the argument

The load-bearing mechanism is the relative energy consumption model $E^r_i = (E^{train}_i + E^{trans}_i)/E^{total,\delta}_i$, where $\delta$ is a per-device sensitivity coefficient, together with a client-selection MDP whose reward multiplies accuracy gain by penalty factors for latency, total energy, and energy variance. The heuristic splits devices into high- and low-ideal-energy clusters, reallocates communication resources via SLSQP, and defines a utility $F(\varphi_i, E_i) = \alpha \varphi_i / (E^{trans}_i + E^{train}_i)$ that discourages over-selection of any device. This heuristic generates state-action pairs used to pre-train the RL agent, which then refines selection online with a target network for stable Q-value updates.

What would settle it

Run BEFL on a physical testbed of the five device types listed in Table I, record actual battery drain and dropout rates over 100 rounds, and check whether energy variance drops by the simulated amount; if the reduction in modeled relative energy does not appear as reduced variance in actual milliampere-hours, the central claim is not supported.

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Extended reading notes

Core claim

The central claim is that energy fairness can be optimized jointly with accuracy and total energy without sacrificing any of them, by treating client selection as a ranking problem learned from a heuristic warm start. In the paper's simulations, BEFL consistently outperforms FedAvg, FedProx, AFL, Favor, and FlashRL: best accuracy reaches 52.46% on non-IID CIFAR-10 and 43.44% on non-IID MNIST, while energy variance drops to as low as 24.6% of the FedAvg baseline. The mechanism is the relative energy consumption model $E^r_i = (E^{train}_i + E^{trans}_i)/E^{total,\delta}_i$, which makes energy-sensitive devices costly to overuse, and a reward function that penalizes energy variance alongside latency and total energy.

Load-bearing premise

The framework's claimed energy gains depend on the simulated relative energy model, with its per-device sensitivity coefficient drawn from a normal distribution, faithfully capturing how real mobile IoT devices drain their batteries.

Editorial extensions

If this is right

Energy fairness can be built into FL client selection without a separate fairness constraint; the variance penalty in the reward suffices.
The heuristic warm start shortens RL convergence, so the method works in training budgets where pure RL would not.
The same reward structure could be applied to other resource-constrained FL settings, such as bandwidth-limited or latency-critical edge networks.
Including relative energy rather than absolute energy in the objective shifts selection away from devices with small battery capacity, which should reduce premature dropout.

Reading between the lines

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

If the relative energy model matches hardware, the framework could adaptively tune $\delta$ per device based on battery state-of-health instead of drawing it from a fixed normal distribution.
The two-cluster heuristic suggests a testable extension: an adaptive number of clusters might better capture multi-modal device populations in larger fleets.
The results imply that total energy and energy variance are partly in tension; real deployments would need to set the penalty thresholds $(T, E, V)$ to match operator priorities.
The reported 72.7% variance reduction is relative to modeled energy; a hardware testbed is needed to confirm the effect transfers to physical battery drain.

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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

You should know two things about this one. First, it tackles a real problem—uneven battery drain that drops devices out of federated learning—and the proposed fix, a cluster-based heuristic that pre-trains an RL client selector, is a sensible extension of the FedRank line. Second, the headline numbers (72.7% variance reduction, 28.2% total energy cut) are produced by the same synthetic energy model that generates the RL reward. That circularity is the thing to check.

The paper's actual contribution is honest: it defines relative energy consumption as Er_i = (Etrain+Etrans)/E_total^δ, where δ is a per-device 'sensitivity coefficient.' I don't know the distribution parameters—they're undisclosed. The evaluation uses this metric throughout. The same E_t and V_t thresholds appear in the reward, and Table II reports variance relative to FedAvg in this same Er space. So the optimizer is directly minimizing the metric being reported. That's not fraud, but it does mean the 72.7% is a property of the model, not of real batteries. The dimensions don't even work for δ≠1: energy divided by battery capacity to the δ is not an energy. Figure 3 labels it KJ/mAh, which only makes sense at δ=1.

On the positive side, the method itself is new: clustering devices by ideal energy consumption and reallocating communication resources is a clean heuristic, and using it to warm-start an RL agent is a practical way to reduce RL sample complexity. The MDP definition is explicit, and the code is promised though I didn't run it. Accuracy gains are modest but consistent across settings, and those come from external datasets, so they're not circular.

Soft spots besides the metric: no seeds, no error bars, no parameter values for reward thresholds or the normal distributions. The headline 72.7% is cherry-picked across baselines and settings. The ablation only shows a loss curve, not quantitative energy numbers. These are fixable.

Bottom line: this paper is for the FL-systems crowd who care about client selection and battery life. The idea is worth reading, but I wouldn't cite its energy claims without an independent validation. If it lands on your desk, send it to review: the problem is real, the approach is coherent, and the flaws are addressable—but the energy model needs to be validated or replaced before the numbers can be trusted.

Referee Report

4 major / 4 minor

Summary. The paper proposes BEFL, a federated-learning client-selection and resource-allocation framework for mobile edge IoT that jointly optimizes global model accuracy, total energy consumption, and energy-consumption variance across devices. The framework combines SLSQP-based communication-resource allocation, a cluster-and-utility heuristic client-selection algorithm, offline imitation learning from that heuristic, and an online ranking-based reinforcement-learning stage. The evaluation is simulation-based on CIFAR-10 and MNIST with 100 virtual clients of heterogeneous hardware, compared against FedAvg, FedProx, AFL, Favor, and FlashRL. The paper reports that BEFL improves accuracy by 1.6%, reduces energy variance by 72.7%, and lowers total energy by 28.2% over existing methods.

Significance. If the energy-balancing claims hold, BEFL addresses a real and under-studied problem: preventing premature dropout of energy-sensitive devices in federated learning. The accuracy results are evaluated on standard external datasets and are not circular, and the combination of SLSQP allocation, heuristic warm-start, and RL is a reasonable design direction. The paper also provides a public code link, which is a useful reproducibility aid. However, the central energy claims are built on a synthetic relative-energy metric that is simultaneously the RL reward signal and the evaluation metric, and no independent physical energy validation is provided; the reported gains therefore are not yet established as real battery-energy improvements.

major comments (4)

[Section II-A3 and Section III-C] The relative energy metric Er_i = (Etrain_i + Etrans_i) / Etotal_i^delta is used both as the evaluation metric for energy consumption and as the objective that the RL reward directly minimizes through the energy and variance thresholds E_t and V_t. The reported 72.7% variance reduction and 28.2% total-energy reduction are therefore reductions of the same modeled quantity that generates the training reward. This is a self-referential evaluation loop: the optimizer may be exploiting properties of the synthetic model rather than balancing real battery drain. The authors should evaluate energy claims with an independent physical energy model, power traces, or hardware measurements, and should report absolute physical energy (J or mAh) alongside the normalized metric.
[Section IV-A2, Section III-B, Section III-C] Several load-bearing parameters are undisclosed: the mean and standard deviation of the normal distribution for the sensitivity coefficient delta, the parameters of the CPU-frequency normal distributions, the penalty thresholds T, E, V, the reward exponents alpha, beta, gamma, and the efficiency factor alpha in the heuristic selection function. Without these values, the experiments cannot be reproduced, and the sensitivity of the reported gains to these choices is unknown. The authors should provide the full parameter settings and a sensitivity analysis for the key thresholds and exponents.
[Table II and Abstract] The three headline percentages in the Abstract are taken from different settings and baselines: the 72.7% variance reduction is BEFL versus FedAvg in the IID CIFAR-10 row (27.3% vs 100%), while the 28.2% energy reduction and the 1.6% accuracy improvement are from the Non-IID CIFAR-10 row (71.8% vs 100% energy, 43.44% vs 41.84% accuracy). The paper should state which baseline and setting each headline number refers to. Moreover, Table II reports single values without error bars, standard deviations, or number of seeds, so the statistical significance of the accuracy and energy differences is not established.
[Section II-A3 and Figure 3] For delta not equal to 1, Er_i has units of energy divided by (battery capacity)^delta, which is neither a physical energy nor a dimensionless fraction. Figure 3 labels the quantity in KJ/mAh, which is only dimensionally valid when delta = 1, yet Section IV-A2 states that delta is drawn from a normal distribution on [0,1] with per-device values. Comparing such heterogeneous quantities across clients makes the reported 'variance' a variance of objects with different units. The authors should either justify the metric, set delta = 1, or report physical energy values for the variance and total-energy claims.

minor comments (4)

[Section II-A3] The formula for relative energy should be written as Er_i = (Etrain_i + Etrans_i) / (Etotal_i)^delta to remove the ambiguity in the denominator notation.
[Section II-B] Constraint (1), Ephi_h >= sum_{theta_i in phi_h}(Etrain_i + Etrans_i), does not appear to impose a meaningful restriction as written; the symbol Ephi_h and the direction of the inequality should be clarified.
[Figure 1 caption] The caption contains a typo: 'energy consumption ensitivity' should be 'energy consumption sensitivity.'
[References] Reference [7] is incomplete; it lists only an author name and a journal title with no article title, volume, or year, and should be completed.

Circularity Check

1 steps flagged · score 6.0 of 10

Energy-variance and total-energy reductions are in-sample: the RL reward and the reported evaluation metric are both the paper's self-defined relative energy Er_i, so the energy claims reduce to the training objective.

fitted input called prediction [Section II-A3; Section III-C; Abstract/Table II]
"We define relative energy consumption as Er_i = (Etrain_i + Etrans_i)/Etotal_i^δ ... The energy consumption mentioned in this article specifically refers to the relative energy consumption under this formula. ... Rewards: We define three rewards—Racc (test accuracy), RT (processing latency), RE (total energy consumption), and RVarE (variance of energy consumption)—to balance multiple objectives during training rounds t: [Rt = ΔRacc_t · ... · (E/Et)^{...} · (V/Vt)^{...}]. Our experiments reveal that BEFL ..."

The paper first declares that 'energy consumption' means the relative quantity Er_i = (Etrain_i + Etrans_i)/Etotal_i^δ. The RL reward terms RE and RVarE then penalize thresholded versions of total energy (E_t) and energy variance (V_t), i.e., exactly this Er_i and its variance. Table II reports 'Energy' and 'Variance' measured on the same modeled Er_i, and Figure 3 plots 'relative energy consumption'. The policy is trained to minimize these quantities, and the headline reductions (72.7% variance, 28.2% total energy) are the resulting values of those same objective terms. They are not independent predictions validated against hardware; the energy claims reduce to the reward function by construction. Accuracy improvements are external and unaffected by this loop.

full rationale

The paper's derivation chain contains one significant self-referential loop. BEFL defines energy consumption as a synthetic relative metric Er_i, uses thresholded total and variance of this metric as RL rewards, and then reports reductions in this same metric as its energy results. That makes the energy-efficiency claims in-sample optimization outcomes rather than empirical predictions; no power traces or physical battery model validate the metric. The accuracy claims (up to 1.6% on CIFAR-10/MNIST) are based on external test data and are not circular. There is no load-bearing self-citation chain: citations to prior work, including one co-authored reference [9] on hierarchical FL scheduling, are background and do not support the central derivation. The score is therefore 6 rather than higher because only the energy portion of the central claim reduces by construction, while the accuracy component stands independently.

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

The framework depends on several hand-chosen or undisclosed parameters (delta, alpha, reward thresholds) and on an ad hoc relative energy metric. No new physical entities are introduced. The energy model is the main external input, and all energy claims are evaluated with that same model.

free parameters (4)

sensitivity coefficient distribution = unspecified, stated range [0,1]
delta is drawn from a normal distribution in [0,1] and appears as an exponent in the relative energy definition; its distribution parameters are not disclosed and it directly affects the reported variance.
efficiency factor alpha in heuristic selection = not specified
alpha < 1 appears in the selection efficiency function F(phi_i, Etrans_i, Etrain_i); the value is never given, and it controls how strongly selection frequency penalizes a client.
reward exponents alpha, beta, gamma and thresholds T, E, V = not specified
These control the penalty applied when latency, energy, or variance exceed thresholds; without their values the reward cannot be reproduced, and tuning them would affect reported gains.
CPU frequency normal distribution parameters = not specified
Real-time CPU frequency is modeled as a normal distribution within hardware ranges, but variance and sampling method are not specified.

assumptions (4)

domain assumption The training energy formula E_train = kappa * I * C * |D| * f^2 * core accurately models device energy consumption.
Used throughout Section II-A to compute every client's training energy; standard in the literature but unvalidated against real hardware here.
ad hoc to paper The relative energy metric Er = (Etrain + Etrans) / E_total^delta captures energy sensitivity and fairness.
This metric is introduced specifically for this paper; the meaning of delta as a 'sensitivity coefficient' and its effect on device dropout are not empirically grounded.
ad hoc to paper The reward function's multiplicative form with thresholds yields the desired trade-off.
No derivation or ablation justifies this reward design; the thresholds and exponents are undisclosed.
standard math OFDMA communication rate formula and transmission energy model are correct.
Standard Shannon-type formula; reasonable but idealizing (no interference) and not validated in the simulator.

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Cite this review

Pith. "Pith review of BEFL: Balancing Energy Consumption in Federated Learning for Mobile Edge IoT." pith.science (2026). https://pith.science/paper/JGTEQABE

@misc{pith2026241203950,
  author       = {Pith},
  title        = {Pith review of: BEFL: Balancing Energy Consumption in Federated Learning for Mobile Edge IoT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JGTEQABE}},
  note         = {Machine review of arXiv:2412.03950}
}

read the original abstract

Federated Learning (FL) is a privacy-preserving distributed learning paradigm designed to build a highly accurate global model. In Mobile Edge IoT (MEIoT), the training and communication processes can significantly deplete the limited battery resources of devices. Existing research primarily focuses on reducing overall energy consumption, but this may inadvertently create energy consumption imbalances, leading to the premature dropout of energy-sensitive devices.To address these challenges, we propose BEFL, a joint optimization framework aimed at balancing three objectives: enhancing global model accuracy, minimizing total energy consumption, and reducing energy usage disparities among devices. First, taking into account the communication constraints of MEIoT and the heterogeneity of devices, we employed the Sequential Least Squares Programming (SLSQP) algorithm for the rational allocation of communication resources. Based on this, we introduce a heuristic client selection algorithm that combines cluster partitioning with utility-driven approaches to alleviate both the total energy consumption of all devices and the discrepancies in energy usage.Furthermore, we utilize the proposed heuristic client selection algorithm as a template for offline imitation learning during pre-training, while adopting a ranking-based reinforcement learning approach online to further boost training efficiency. Our experiments reveal that BEFL improves global model accuracy by 1.6\%, reduces energy consumption variance by 72.7\%, and lowers total energy consumption by 28.2\% compared to existing methods. The relevant code can be found at \href{URL}{https://github.com/juzehao/BEFL}.

Figures

Figures reproduced from arXiv: 2412.03950 by the authors.

**Figure 1.** The two issues in energy consumption optimization for FL: 1) The impact of device heterogeneity on energy consumption ensitivity. 2) The imbalance in energy consumption among devices. training and data communication. Ignoring these differences can result in excessive reliance on energy-hungry devices, increasing overall energy consumption and causing workload imbalances. To mitigate these issues, Cui et al. [9] desi… view at source ↗

**Figure 2.** BEFL framework overview: 1. The server retrieves hardware information from devices. 2. It simulates energy consumption and latency using energy consumption model. 3. Client selection is facilitated by a heuristic algorithm. 4. Generated state-action pairs are sent to the RL network for pre-training. 5-11. During online training, the RL agent gathers state information, selects clients, conducts local training, aggreg… view at source ↗

**Figure 4.** The variation of loss values for various algorithms under the NonIID setting of CIFAR10 To demonstrate the role of the proposed heuristic algorithm in the warm-up phase of imitative learning, we compare three algorithms: RL, the RL algorithm without pre-training; AFL+RL, the RL algorithm pre-trained using AFL; and BEFL, the RL algorithm pre-trained with the proposed heuristic algorithm. As shown in [PITH_FULL_IMA… view at source ↗

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