Hierarchical Federated Learning Across Heterogeneous Cellular Networks

Mehdi Salehi Heydar Abad; Emre Ozfatura; Deniz Gunduz; Ozgur Ercetin

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Hierarchical Federated Learning Across Heterogeneous Cellular Networks

Mehdi Salehi Heydar Abad, Emre Ozfatura, Deniz Gunduz, Ozgur Ercetin

arXiv:1909.02362v1Sep 5, 2019cs.LGcs.DCcs.ITeess.SPstat.ML

TL;DR

Wireless data offloading for centralized ML is constrained by latency, bandwidth, and privacy. The paper introduces hierarchical FEEL over HCNs, combining SBS-level orchestration with periodic MBS consensus, gradient sparsification, periodic averaging, and resource allocation. CIFAR-10 results show dramatically lower communication latency without sacrificing much model accuracy.

Problem
Centralized ML cannot always feasibly offload distributed wireless-device datasets because of latency, bandwidth, and privacy constraints, while HCN implementations of communication-efficient FL remain insufficiently addressed.
Method
The paper clusters MUs around SBSs for local distributed SGD, periodically exchanges model updates with the MBS, and jointly uses gradient sparsification, periodic averaging, and resource allocation.
Results
CIFAR-10 experiments show that the hierarchical approach dramatically reduces communication latency without sacrificing much accuracy.
Takeaways & Limitations
Hierarchical FEEL can reduce communication latency in large-scale HCN-based distributed image classification while retaining model accuracy.

Abstract

from arXiv · show

We study collaborative machine learning (ML) across wireless devices, each with its own local dataset. Offloading these datasets to a cloud or an edge server to implement powerful ML solutions is often not feasible due to latency, bandwidth and privacy constraints. Instead, we consider federated edge learning (FEEL), where the devices share local updates on the model parameters rather than their datasets. We consider a heterogeneous cellular network (HCN), where small cell base stations (SBSs) orchestrate FL among the mobile users (MUs) within their cells, and periodically exchange model updates with the macro base station (MBS) for global consensus. We employ gradient sparsification and periodic averaging to increase the communication efficiency of this hierarchical federated learning (FL) framework. We then show using CIFAR-10 dataset that the proposed hierarchical learning solution can significantly reduce the communication latency without sacrificing the model accuracy.

I. INTRODUCTION

The paper develops hierarchical federated learning for heterogeneous cellular networks to address communication and privacy constraints in distributed ML. It combines sparsification, periodic averaging, and resource allocation to reduce latency while largely preserving accuracy.

Centralized ML is often impractical because wireless offloading faces latency and bandwidth constraints, while datasets may contain sensitive personal information.
Existing communication-efficient FL techniques have not fully addressed implementation and orchestration over heterogeneous cellular networks.
The proposed framework clusters mobile users around SBSs for local distributed SGD and periodically exchanges models with the MBS for global consensus.
The framework jointly employs gradient sparsification and periodic averaging, with resource allocation designed to minimize end-to-end latency.
CIFAR-10 experiments show dramatically reduced communication latency in large-scale FEEL over HCNs without sacrificing much accuracy.
In synchronous FL, the MBS waits for gradients from all MUs, aggregates them, and transmits the average gradient back to the users.

A. Uplink Latency

The uplink latency analysis models practical wireless transmission from mobile users to the MBS and optimizes carrier allocation and power thresholds to improve aggregation rates.

Truncated channel inversion allocates power only when the channel gain exceeds a threshold, providing a practical fixed-rate transmission policy.
The power allocation satisfies average power constraints based on observed channel gains and channel-gain statistics.
The analysis uses M-ary QAM with a target BER to determine instantaneous uplink rates on assigned sub-carriers.
Each MU transmits Q · ˆQ quantized gradient bits, so carrier allocation maximizes the minimum average uplink rate across users.

B. Downlink Latency

The downlink broadcasts the aggregated gradient from the MBS to all mobile users using a rate constrained by the weakest instantaneous channel. The per-iteration FL latency combines uplink and downlink transmission times.

After collecting gradients, the MBS averages them and broadcasts the common result to all mobile users.
The broadcast uses rateless coding adapted to the worst instantaneous SNR on each sub-carrier, with MBS power uniformly distributed across sub-carriers.
The downlink ends after all Q · ˆQ parameters are received by the workers.
Per-iteration end-to-end FL latency is defined as T_F_L = T_UL + T_DL.

C. Sub-carier Allocation Policy

The proposed sub-carrier allocation algorithm initializes one sub-carrier per mobile user, then repeatedly assigns remaining sub-carriers to the user with the minimum average uplink rate. Theorem 1 establishes that this policy is optimal.

Algorithm 2 assigns one sub-carrier to each mobile user before allocating remaining sub-carriers.It then optimizes each user’s threshold and identifies the user with the minimum average uplink rate.
Remaining sub-carriers are allocated iteratively to the mobile user with the minimum average uplink rate.After each allocation, that user’s threshold and average rate are updated.
The allocation procedure continues until all available sub-carriers are assigned.
Theorem 1 states that the sub-carrier allocation policy in Algorithm 2 is optimal.
The proof uses induction over the number of allocated sub-carriers, showing that assigning the next carrier to the minimum-rate user is optimal.The base case begins with K+1 sub-carriers, and the induction step considers one additional carrier.

III. DISTRIBUTED HIERARCHICAL FEDERATED LEARNING

The hierarchical federated learning framework clusters mobile users around small-cell base stations for local aggregation, while periodically averaging cluster models through the macro base station to maintain global consensus. This reduces communication distance and latency but requires inter-cluster averaging to avoid separate cluster models.

Mobile users send local gradient estimates to their cluster’s small-cell base station instead of directly to the macro base station.Each small-cell base station aggregates the cluster gradients and returns the average to its associated users.
Clustered gradient communication reduces communication distance and latency while enabling spatial reuse of communication resources.Restricting communication within clusters can otherwise prevent convergence to a single global model.
After every H intra-cluster iterations, small-cell base stations send their local models to the macro base station for global averaging.The averaged model is transmitted back through the small-cell base stations to all mobile users.
During each intra-cluster iteration, mobile users compute local gradient estimates and transmit them to the small-cell base station serving their cluster.
Algorithm 3 implements local updates, periodic small-cell-to-macro aggregation, and redistribution of the global model.

A. Communication Latency analysis

The latency analysis models hierarchical communication with spatially separated, color-coded clusters that reuse sub-carriers, while accounting for local aggregation and periodic global model averaging. It expresses fronthaul latency through the uplink and downlink rates between small-cell and macro base stations.

Clusters using the same color are separated by at least Dth, allowing sub-carriers to be divided among colors to reduce interference.The analysis assumes zero interference for receivers beyond Dth.
The latency analysis assumes uniformly distributed mobile users, equal users per cluster, and small-cell base stations located at cluster origins.
Local gradient-update latency is analyzed similarly to federated learning, but each cluster uses M/Nc sub-carriers and mobile users transmit to small-cell base stations.
Figure 1 distinguishes local gradient updates from global model averaging in the hierarchical procedure.
At each hierarchical period, small-cell base stations exchange averaged models with the macro base station over uplink and downlink fronthaul links.The corresponding period includes model transmission to the macro base station, averaging, return transmission, and delivery to mobile users.

IV. SPARSE COMMUNICATIONS

Sparse communication reduces transmitted gradient content by selecting only sufficiently large accumulated updates, while error accumulation and momentum correction address delayed gradients and stale momentum. The resulting sparse federated SGD procedure transmits masked updates instead of full gradients.

Sparsification transmits only a fraction of gradient elements to reduce communication latency for large neural-network models.
An error-buffer vector v accumulates gradients that are not transmitted so they can be sent in later iterations.The accumulated unsent gradients grow over time and are eventually transmitted.
Sparse federated SGD uses momentum accumulation, a magnitude threshold, and a mask to select transmitted gradient elements.The algorithm sends the masked update and retains masked-out components for subsequent updates.
Each mobile user transmits sparse(vk,t) rather than the full gradient gk,t to the macro or small-cell base stations.
Momentum updates use σ as the momentum parameter and g as the aggregated gradient.
Inverted sparsification is applied to accumulated gradients and the momentum factor to address staleness caused by delaying small gradients.A mask prevents stale momentum terms from being applied.

A. Sparse Communication and Error Accumulation

The framework sparsifies each of its four communication steps and uses error accumulation to mitigate the resulting model error. It transmits model differences relative to reference models during hierarchical averaging.

Sparse communication: Four communication steps use separate sparsification parameters to reduce communication overhead.The steps are MU–SBS uplink, SBS–MU downlink, SBS–MBS uplink, and MBS–SBS downlink.
Sparse communication: Ω(V, φ) maps a d-dimensional vector to a sparse vector with only 1 −φ indices nonzero.
Error accumulation: Discounted error accumulation compensates for sparsification errors that otherwise slow convergence.The method carries discounted model errors into subsequent updates.
Error accumulation: Reference models let SBSs transmit model differences to the MBS and MUs instead of transmitting full models.The references are maintained separately for the MBS and each SBS.

V. NUMERICAL RESULTS

The numerical-results section presents the hierarchical federated-learning algorithm and its cellular simulation setting. The setup uses clustered users, specified wireless parameters, and periodic model exchange between SBSs and the MBS.

Network topology: The simulation uses seven hexagonal clusters in a 750-meter-radius area with a 500-meter inscribed-circle diameter.
Algorithm: Algorithm 5 initializes global, SBS, and user models before iterative local training and hierarchical aggregation.
Algorithm: Users compute stochastic gradients, apply threshold-based masking, and send sparse updates to their associated SBS.
Algorithm: SBS models are updated locally, and every H iterations their model differences are sparsified and sent to the MBS.
Simulation parameters: The setup specifies 300 subcarriers at 30 KHz spacing, with maximum powers of 20 W for the MBS, 6.3 W for SBSs, and 0.2 W for MUs.

B. Implementation guideline

The implementation evaluates ResNet18 image classification on CIFAR-10 and uses large-batch training techniques alongside a specified training configuration. Figure 3 examines latency speed-up for hierarchical versus conventional FL.

Implementation: The experiments train ResNet18 for CIFAR-10 image classification with 10 image classes.
Implementation: Data remain assigned to the same mobile-user subsets without shuffling, with per-user batch size β = 64.
Implementation: Large-batch training uses learning-rate scaling and a warm-up phase.
Implementation: The fronthaul link is assumed to be 100 times faster than the mobile-user uplink and downlink.
Numerical results: Figure 3 reports latency speed-up of HFL versus FL, with speed-up defined as T_FL/Γ_HFL.

C. Results

HFL improves communication latency through hierarchical aggregation, clustering, and sparsification while maintaining comparable CIFAR-10 accuracy. Its accuracy may be further improved through momentum correction, and broader settings remain future work.

HFL achieves good latency speedup over FL, improving as the inter-cluster averaging period increases.The comparison varies mobile users per cluster and periods H = 2, 4, 6.
Clustering increases latency speedup as the path-loss exponent becomes more severe.Clustering reduces communication distance and improves SNR relative to centralized communication over longer paths.
Sparsification significantly improves latency for both FL and HFL, with HFL more robust as the number of mobile users increases.The macro cell’s greater user load makes resource scarcity more consequential than in small cells.
HFL latency speedup does not compromise CIFAR-10 model accuracy, and HFL achieves better accuracy than FL across the reported situations.The experiments use ResNet 18 and average accuracy over five runs.
The authors attribute a small accuracy degradation in hierarchical learning mainly to local momentum SGD and sparsification.They suggest global or momentum-averaging corrections as possible improvements.
The study plans to extend evaluation to non-IID mobile-user data, batch-size adaptation, and training time including mobile-user computation.These directions are identified as future work rather than evaluated results.