Source-linked AI summary
Scheduling for Cellular Federated Edge Learning with Importance and Channel Awareness
Jinke Ren, Yinghui He, Dingzhu Wen, Guanding Yu, Kaibin Huang, Dongning Guo
TL;DR
The paper addresses a bottleneck to fast FEEL and proposes importance- and channel-aware scheduling. Its framework targets unbiased aggregation, incorporates channel state and update importance, extends to multiple-device scheduling, and reports performance gains over benchmark policies.
Problem
The paper addresses a bottleneck to fast FEEL that calls for effective scheduling.
Method
The paper develops a probabilistic scheduling framework for unbiased update aggregation, designs channel- and update-aware scheduling, and extends it to multiple-device scheduling.
Results
The proposed scheduling policy achieves a performance gain compared with benchmark policies.
Takeaways & Limitations
The framework combines channel state and update importance while supporting unbiased aggregation and multiple-device scheduling.
Abstract
from arXiv · showhide
In cellular federated edge learning (FEEL), multiple edge devices holding local data jointly train a neural network by communicating learning updates with an access point without exchanging their data samples. With very limited communication resources, it is beneficial to schedule the most informative local learning updates. In this paper, a novel scheduling policy is proposed to exploit both diversity in multiuser channels and diversity in the "importance" of the edge devices' learning updates. First, a new probabilistic scheduling framework is developed to yield unbiased update aggregation in FEEL. The importance of a local learning update is measured by its gradient divergence. If one edge device is scheduled in each communication round, the scheduling policy is derived in closed form to achieve the optimal trade-off between channel quality and update importance. The probabilistic scheduling framework is then extended to allow scheduling multiple edge devices in each communication round. Numerical results obtained using popular models and learning datasets demonstrate that the proposed scheduling policy can achieve faster model convergence and higher learning accuracy than conventional scheduling policies that only exploit a single type of diversity.
I. INTRODUCTION
FEEL reduces privacy concerns by keeping data at distributed edge devices while aggregating local learning updates, but wireless communication limits training speed. The paper motivates scheduling that jointly considers channel conditions and the unequal importance of local updates.
- FEEL trains a shared model across distributed edge devices while reporting local updates instead of raw data.
- Wireless communication is a major bottleneck because channel fading, interference, and noise constrain fast update acquisition.
- Conventional scheduling emphasizes data rate or quality of service while assuming transmitted updates are equally important.
- Local learning updates have dissimilar significance for model convergence, motivating importance-aware scheduling in FEEL.
- The paper jointly exploits diversity in wireless channels and local learning updates through channel-and-update-aware scheduling.
B. Contributions and Organization
The paper develops an importance- and channel-aware FEEL scheduling policy, extending probabilistic selection from one device to multiple devices per round. It also provides convergence analysis and evaluates gains over conventional schemes.
- Contributions: The proposed probabilistic scheduling framework yields unbiased gradient aggregation in FEEL and measures update importance by gradient divergence.
- Contributions: For one scheduled device per round, scheduling probability increases with data imbalance and local gradient norm while decreasing sublinearly with upload latency.
- Contributions: The framework extends to multiple devices per round using an efficient without-replacement scheduling algorithm and closed-form bandwidth allocation.
- Contributions: Numerical results demonstrate performance gains over conventional scheduling schemes.
- System model: The FEEL system collaboratively trains a shared model from distributed local datasets while preserving data privacy through local-gradient reporting.
- System model: Only a small subset of devices can participate in each global gradient aggregation because of communication-resource limitations.
C. Communication Model
The communication model allocates uplink bandwidth across OFDMA sub-channels and schedules device updates through an edge-server-controlled FEEL protocol. Training time depends on both communication latency and the model variation produced by selected gradients.
- Communication model: OFDMA divides system bandwidth into interference-free sub-channels allocated across devices for uplink communication.
- Communication model: A device’s uplink rate depends on its allocated bandwidth and uplink SNR, which reflects transmit power, channel gain, and noise power.
- Learning mechanism: The edge server broadcasts the global model, selects devices, allocates bandwidth, and solicits their local updates.
- Learning mechanism: Selected devices upload local gradients, after which the server computes the global gradient and updates the model.
- Scheduling principle: Training time is determined by one-round latency and model variation, both of which are affected by scheduling decisions.
- Scheduling principle: The scheduling design balances channel diversity, which affects latency, with update diversity, which affects model variation.
B. Probabilistic Scheduling
The paper introduces probabilistic scheduling to preserve unbiased global-gradient aggregation while allowing nonuniform device-selection probabilities. Its convergence analysis links scheduling-dependent gradient variance to learning progress and motivates gradient divergence as an importance measure.
- Probabilistic scheduling: Probabilistic scheduling selects devices according to a distribution while scaling received local gradients before aggregation.Every device must have nonzero selection probability for the unbiasedness guarantee.
- Unbiased aggregation: The aggregated global gradient is an unbiased estimate of the ground-truth global gradient under the proposed framework.The result follows by taking expectation over the scheduling distribution.
- Convergence analysis: The one-round expected loss gap is bounded by the previous gap, the squared global-gradient norm, and aggregated-gradient variance.The first two terms are independent of scheduling, whereas the variance term depends on the scheduling design.
- Convergence analysis: Smaller aggregated-gradient variance corresponds to faster global-loss decrease because the ground-truth gradient gives the steepest loss-decrease direction.This connects scheduling design directly to the convergence rate.
- Gradient importance measurement: Gradient divergence measures the deviation between a scaled local gradient and the ground-truth global gradient, with smaller divergence indicating greater contribution to convergence.It is introduced as the local-update importance measurement.
D. One-Round Latency Analysis
The scheduling design accounts for both device learning-update importance and one-round latency. Because the best channel and smallest gradient divergence rarely coincide, the policy optimizes their weighted trade-off.
- Latency model: Training performance depends on gradient importance and one-round latency, making latency an essential scheduling consideration.The one-round latency includes global-model broadcast, local-gradient calculation, and local-gradient upload components.
- Channel–importance trade-off: The desired device has both the best channel state and the smallest gradient divergence, but this combination rarely occurs in practice.The resulting conflict creates a trade-off between update quality and communication delay.
- Channel–importance trade-off: The objective weights gradient divergence against one-round latency using ρ ∈ [0, 1].The weight can be chosen so the two weighted quantities have the same order.
- Optimal scheduling policy: The optimal one-device scheduling probability is derived from the trade-off problem through Theorem 1.The solution uses an optimal Lagrangian multiplier λ_t* obtained by one-dimensional search.
- Optimal scheduling policy: For fixed λ_t*, scheduling probability increases with data-unbalanced indicator and local-gradient norm, but decreases when upload latency is large.The data-unbalanced indicator represents each device’s local-dataset share in the global dataset.
- Practical implementation: The policy uses gradient norm and local dataset size to characterize importance, while channel estimation supplies upload latency for joint scheduling.This enables practical exploitation of both update and channel diversity.
B. Convergence Analysis
Under Lipschitz-gradient and strong-convexity assumptions, the proposed policy admits convergence bounds. With suitable learning rates, the expected loss gap and the policy’s cumulative impact approach zero.
- Convergence upper bound: Theorem 2 bounds the expected global-loss gap by the initial gap and the cumulative impact of the proposed scheduling policy.The bound is stated for the scheduling policy given in Theorem 1.
- Convergence upper bound: When 0 < η_i < 1/(2µ), the initial-gap term and the weighted cumulative scheduling term both approach zero as communication rounds increase.The weight coefficient A_i decreases with the round index.
- Convergence upper bound: The learning model therefore converges to the optimum under the proposed scheduling solution.This conclusion is derived from the convergence upper bound under the stated learning-rate condition.
- Learning convergence rate: With a diminishing learning rate, Corollary 1 characterizes the learning convergence rate over T communication rounds.The analysis also relates convergence to the gradient norm across communication rounds.
- Learning convergence rate: Increasing the total number of communication rounds leads to learning convergence.The stated convergence-rate result provides the analytical basis for this conclusion.
V. SCHEDULING MULTIPLE DEVICES IN EACH ROUND
The probabilistic framework is extended to schedule multiple devices without replacement in each communication round. The paper supplies an unbiased aggregation result and a lower-complexity sequential scheduling algorithm with bandwidth-allocation support.
- Practical implementation: The multiple-device design also proposes optimal bandwidth allocation for practical implementation.This extends the scheduling treatment beyond device selection alone.
- Multiple-device probabilistic scheduling: Multiple-device scheduling selects a device sequence without replacement and retains the probabilistic scheduling framework.The selected devices are drawn sequentially according to conditional distributions.
- Unbiased aggregation: The average of the selected local gradients is an unbiased estimate of the ground-truth global gradient.Each selected local gradient is shown to be unbiased under the conditional scheduling distributions.
- Scheduling algorithm: The practical algorithm sequentially selects M devices, updating the candidate distribution after each selection.It assumes the entire bandwidth is available to each device during sequential selection.
- Scheduling algorithm: The sequential algorithm sacrifices optimality to significantly reduce computational complexity.Its complexity is characterized using the number of scheduled devices and the tolerance of the one-dimensional multiplier search.
B. Bandwidth Allocation
The bandwidth allocation minimizes overall gradient-upload latency for a selected device sequence. Its optimum equalizes local gradient upload latency across scheduled devices, assigning more bandwidth to worse channels.
- The allocation problem minimizes overall gradient upload latency because broadcast and local gradient calculation latencies are bandwidth-independent.The resulting optimization is convex and can be solved using KKT conditions.
- The optimal allocation equalizes local gradient upload latency among all scheduled devices.
- Given a scheduled device sequence, Theorem 3 provides the optimal bandwidth allocation for reporting local gradients.
- More bandwidth is allocated to devices with worse channel states to achieve the smallest one-round latency.Equalized communication latency facilitates the update synchronization required for gradient aggregation.
VI. NUMERICAL RESULTS
Experiments evaluate the scheduling policies using SVM and CNN classifiers under non-IID device data. The proposed importance- and channel-aware policy consistently outperforms single-diversity baselines, with gains becoming especially clear for CNN training and higher target accuracy.
- SVM results: The proposed policy initially matches channel-aware convergence with ρ = 5 × 10^-6, then surpasses it as training proceeds.Early in training, channel state is dominant because devices' updates play similar roles in convergence.
- SVM results: The proposed policy outperforms importance-aware scheduling because it balances channel state and update importance throughout training.
- SVM results: An excessively large ρ produces marginal gains by limiting exploitation of channel diversity, so the coefficient must be selected carefully.
- CNN results: The proposed policy consistently surpasses channel-aware and importance-aware scheduling for the CNN model.The authors describe this as confirming robustness and stability against model structure.
- CNN results: 60 minutes versus 123 minutes: the proposed policy reaches 0.8 accuracy in less than half the time required by importance-aware scheduling.
- CNN results: Channel-aware scheduling cannot achieve 0.9 target accuracy because devices with poor channels contribute insufficient data information.The performance gap is larger for multiclass CNN classification, where update diversity is greater.
C. Scheduling Multiple Devices in Each Round
The proposed policy achieves the fastest convergence and highest learning accuracy when scheduling multiple devices, while adapting device number to wireless conditions improves performance.
- The proposed policy achieves the fastest convergence speed and highest learning accuracy throughout training for both SVM and CNN experiments.The experiments use real datasets and evaluate multiple-device scheduling with SVM and CNN models.
- Channel-aware scheduling overlooks update importance, whereas importance-aware scheduling is unconscious of channel conditions.
- The proposed sequential scheduling without replacement is applicable even though it cannot guarantee optimal device scheduling.
- The performance improvement is more conspicuous for multiple-device scheduling than for one-device scheduling, supporting a quality–quantity trade-off in update aggregation.
- With small bandwidth B = 1 MHz, scheduling one device converges faster without sacrificing accuracy, while with large bandwidth B = 20 MHz, scheduling 10 devices is superior in convergence speed.These comparisons are reported for the SVM model across different scheduled device numbers.
- The device-number selection criterion should adapt to the wireless environment because scheduling multiple devices can reduce global gradient variance and accelerate training under resource guarantees.
APPENDIX A PROOF OF LEMMA 2
The proof establishes the one-round convergence result by combining convexity, the global model update, gradient unbiasedness, and a bound involving global-gradient variance.
- The auxiliary function is shown to be convex by examining its second-order partial derivative.
- Applying the global model update to the convexity relation yields an inequality for the next iterate.
- Taking expectations uses the variance of the global gradient and the fact that the aggregated gradient is an unbiased estimate of the ground-truth gradient.
- Subtracting E{L(w∗)} produces the one-round convergence rate stated in Lemma 2.
APPENDIX D PROOF OF COROLLARY 1
The proof of Corollary 1 uses induction under the specified diminishing learning-rate assumption and a bounded global-gradient norm.
- The proof proceeds by induction, beginning with an inequality that holds in every communication round.
- The learning rate is assumed to follow η_t = χ t + ν with χ > 1.
- The induction step defines G as an upper bound on the global gradient norm and shows the desired result persists from t = N to t = N + 1.