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FedPGT: Progressive Gradient Transmission for Vehicular Federated Learning over Time-Varying Channels
Jintao Yan, Tan Chen, Yuxuan Sun, Sheng Zhou, Zhisheng Niu
TL;DR
Vehicular federated learning faces fluctuating communication conditions that make predetermined sparsification ill-suited to changing transmission opportunities. FedPGT progressively transmits high-magnitude gradient entries and uses online resource allocation; it improves reported results on CIFAR-10 and Argoverse relative to state-of-the-art benchmarks.
Problem
Vehicle mobility makes channel conditions and transmission capacity vary rapidly, while fixed sparsification decisions and fixed-participation analyses do not match these changing communication opportunities.
Source: §I · p. 1Method
FedPGT progressively transmits high-magnitude gradient entries under instantaneous conditions and uses surrogate variables with Lyapunov optimization for online scheduling and resource allocation.
Source: §I · pp. 1–2Results
3.65% higher test accuracy on CIFAR-10 and 12.66% lower average displacement error on Argoverse than state-of-the-art benchmarks.
Source: §I · p. 2Takeaways & Limitations
Increasing transmitted gradient entries yields diminishing convergence gains, and a small number of high-magnitude entries can preserve most of that gain.
Source: §I · p. 2
Abstract
from arXiv · showhide
Vehicular federated learning (VFL) enables privacy-preserving collaborative model training for intelligent transportation systems, where communication resource allocation and gradient sparsification techniques have been explored to reduce communication overhead. However, vehicle mobility leads to rapidly varying channel conditions and transmission capacity, rendering predetermined resource allocation and sparsification decisions ineffective. In this paper, we propose FedPGT, a progressive gradient transmission scheme for VFL over time-varying channels, where vehicles progressively transmit high-magnitude gradient entries in response to instantaneous channel conditions. We establish a convergence bound that characterizes the impact of transmitted gradient entries and reveals diminishing-return behavior governed by a power-law decay. Motivated by this result, we formulate a stochastic optimization problem for online decision-making, where the main challenge lies in a cumulatively coupled, non-separable objective. To handle this challenge, we introduce per-slot surrogate transmission variables to decouple the long-term dependence across time slots and convert the original objective into an additive per-slot optimization problem, enabling a Lyapunov drift-plus-penalty approach for online scheduling. We further develop a low-complexity resource allocation algorithm for efficient online implementation. Experimental results demonstrate that the proposed scheme achieves a 3.65% accuracy improvement on the CIFAR-10 image classification task and a 12.66% reduction in average displacement error on the Argoverse trajectory prediction task compared with state-of-the-art baselines, demonstrating its applicability to diverse learning tasks under highly dynamic vehicular environments.
I. INTRODUCTION
FedPGT adapts gradient transmission to changing vehicle channels and participation, addressing the limits of predetermined sparsification. The introduction situates this approach in vehicular federated learning and reports improvements on image-classification and trajectory-prediction tasks.
I. INTRODUCTION
- Vehicle mobility causes short RSU sojourns and fluctuating uplink capacity, while fixed sparsification and fixed-client analyses do not fit changing participation and transmission opportunities.Source: §I · p. 1
- FedPGT progressively sends high-magnitude gradient entries according to instantaneous communication conditions, adapting transmission to time-varying channels and vehicle participation.Source: §I · p. 1
- Increasing transmitted gradient entries improves convergence with power-law diminishing returns, so a small number of high-magnitude entries can preserve most convergence gain.Source: §I · p. 2
- 3.65% higher CIFAR-10 test accuracy and 12.66% lower Argoverse average displacement error than state-of-the-art benchmarks demonstrate results across two learning tasks.Source: §I · p. 2
A. Federated Learning in Vehicular Networks
- Existing vehicular FL work addresses mobility, scheduling, and slot-level resource allocation, but does not model progressive within-round transmission of dominant gradient entries under fast channel fluctuations.Source: A. Federated Learning in Vehicular… · p. 2
B. Compression and Sparsification in Federated Learning
- Prior compression and joint scheduling methods generally set sparsification structure or degree before transmission or at round boundaries, rather than adapting within a round to fast channel changes.Source: B. Compression and Sparsification in… · pp. 2–3
A. VFL Model
- An RSU coordinates training across rounds for vehicles with local datasets drawn from their respective data distributions; vehicle participation can vary over time.Source: A. VFL Model · p. 3
1) Local Updates:
- Each round includes local updates, gradient uploading, and model aggregation; vehicles compute stochastic gradients using SGD on mini-batches sampled from local data.Source: A. VFL Model · p. 3, 1) Local Updates · p. 3
2) Gradient Uploading:
Vehicles upload gradient updates progressively to the RSU, which aggregates received updates and proceeds to the next training round. The model describes local computation and uplink communication over discrete slots.
2) Gradient Uploading:
- Vehicles progressively transmit dominant gradient entries to the RSU, which aggregates uploaded gradients and proceeds to the next round.Source: 2) Gradient Uploading · p. 3, 3) Model Aggregation · p. 3
B. Computation Model
- Local training uses a standard computation model based on the floating-point operations required per sample and each vehicle’s CPU clock frequency.Source: B. Computation Model · p. 3
C. Communication Model
- The vehicular network uses OFDMA over discrete time slots, with uplink resource blocks allocated to vehicles for gradient uploads.Source: C. Communication Model · p. 4
- The RSU uses maximal-ratio combining for uplink reception, while downlink model-distribution latency is ignored.Source: C. Communication Model · p. 4
D. Progressive Gradient Transmission
FedPGT lets vehicles upload dominant gradient entries as communication opportunities arise. Its convergence analysis links the number of uploaded entries to gradient approximation error and shows diminishing returns from transmitting more entries.
D. Progressive Gradient Transmission
- Vehicles progressively upload dominant gradient entries over available communication opportunities, with the number of new entries capped by each slot’s achievable rate and entry overhead.Source: D. Progressive Gradient Transmission · p. 4
A. Convergence Analysis
- The gradient approximation error bound varies with the number of uploaded entries, and the resulting convergence bound applies after R training rounds.Source: A. Convergence Analysis · p. 5
- Increasing uploaded entries improves convergence with diminishing marginal returns under the power-law term, so a small set of dominant entries captures most of the benefit.Source: A. Convergence Analysis · p. 5
B. Problem Formulation
The formulation minimizes a convergence upper bound through communication allocation, but its cumulative coupling and unknown future conditions prevent direct slot-wise optimization. A surrogate reformulation and Lyapunov queues convert it into per-slot decisions while tracking energy and transmission consistency.
B. Problem Formulation
- The formulation minimizes the convergence upper bound by optimizing communication resource allocation, with RB and power strategies represented across the round.The constraints impose a vehicle energy budget, require transmission to start after local training, and restrict feasible transmission and power allocations.Source: B. Problem Formulation · p. 5
- Vehicles face uncertain future channel states and availability, while integer and coupled decisions make the original stochastic problem difficult even with perfect future information.Mobility also causes rapidly varying communication conditions and unpredictable system evolution.Source: A. Transformation of the Stochastic… · pp. 5–6
- The original objective is cumulatively coupled across slots, so the authors upper-bound it with an additively separable surrogate that enables Lyapunov per-slot optimization.Surrogate variables represent slot-wise contributions to cumulative transmitted entries, with a long-term equality enforcing consistency with actual transmissions.Source: A. Transformation of the Stochastic… · p. 6
- Virtual energy and PGT queues enforce long-term energy limits and consistency between surrogate transmission variables and actual transmitted entries.The PGT backlog measures accumulated discrepancy and reduces transmission incentive as diminishing marginal convergence gains accrue.Source: A. Transformation of the Stochastic… · p. 6
A. Transformation of the Stochastic Optimization Problem
- The drift-plus-penalty transformation produces a separable per-slot problem decomposed into resource allocation and auxiliary-variable optimization.P3 determines current-slot RB and power decisions, while P4 separately optimizes the auxiliary variable.Source: A. Transformation of the Stochastic… · pp. 6–7
- The online policy has a bounded gap to the offline optimum and bounded long-term energy consumption when each decomposed per-slot problem is solved optimally.The theorem assumes virtual queues are initialized to zero.Source: A. Transformation of the Stochastic… · p. 7
- P4 is convex with a convex feasible set, so its optimal auxiliary-variable solution follows from KKT conditions.P3 remains a MINLP because of binary RB variables and nonlinear coupling from power constraints.Source: A. Transformation of the Stochastic… · p. 7
B. RB Allocation Criterion
The RB criterion uses relaxed allocation and utility-based optimality conditions to identify candidate assignments, while preserving exclusive allocation as an optimal solution for fixed power.
B. RB Allocation Criterion
- A necessary KKT-based condition for positive RB allocation provides the basis for the proposed allocation criterion, although it does not directly yield a global optimum.The relaxation allows RB allocation variables to vary continuously between zero and one.Source: B. RB Allocation Criterion · p. 7
- For fixed power, the relaxed RB allocation problem admits an integral optimum assigning each RB exclusively to one vehicle.Vehicles are eligible only after completing local training; the relaxed problem remains non-convex in allocation and power.Source: B. RB Allocation Criterion · p. 7
- For each RB, the relaxed subproblem has an integral solution because allocating the RB to one vehicle is no worse than leaving it unassigned.Among vehicles tied at the minimum utility, the objective contribution is unchanged by how allocation weights are distributed, provided they sum to one.Source: B. RB Allocation Criterion · p. 8
C. Power Allocation
Given an RB assignment, the paper characterizes optimal transmit power and uses an incremental channel-gain-ordered search to identify the RB subset receiving positive power.
C. Power Allocation
- Given an RB allocation, the optimal transmit power for each vehicle is characterized by a closed-form expression.The expression depends on identifying the subset of RBs assigned positive power.Source: C. Power Allocation · p. 8
- The power-allocation algorithm sorts candidate RBs by descending channel gain and adds them sequentially until a non-positive power value appears.Only RBs receiving positive power remain in the selected subset.Source: C. Power Allocation · p. 8
- The PGT and energy queue backlogs regulate transmission urgency and power use: nonnegative PGT backlog yields zero power, while larger energy backlog penalizes future power allocation.When PGT backlog is negative, the system allocates more communication resources to increase transmitted gradient entries.Source: C. Power Allocation · p. 8
D. Joint RB and Power Allocation Algorithm
The joint allocator iteratively couples RB assignment with power recomputation, and the overall online procedure uses current channel and queue observations to adapt transmission. The simulations use urban vehicular settings and evaluate image classification and trajectory prediction.
D. Joint RB and Power Allocation Algorithm
- The joint RB and power algorithm addresses their coupling by iteratively assigning RBs according to marginal utility under adaptive power allocation.It recomputes candidate power allocations, selects the RB-vehicle pair with the smallest utility value, and finalizes power after assignment.Source: D. Joint RB and Power Allocation… · pp. 8–9
E. The Overall Procedure of FedPGT
- Per-slot execution solves the decomposed problems using observed channel states and queue values, then vehicles transmit and update virtual queues.The procedure estimates compressibility locally and adapts without requiring future system information; it achieves a bounded performance gap.Source: E. The Overall Procedure of FedPGT · p. 9, D. Joint RB and Power Allocation… · p. 9
- The per-slot complexity is O(N^(r)Z^2), yielding O(TN^(r)Z^2) over T slots.The RB assignment dominates; P4 scales linearly with vehicle count.Source: E. The Overall Procedure of FedPGT · p. 9
A. Simulation Setups
- The evaluation uses SUMO-generated urban grid roads with a central RSU and tests CIFAR-10 classification and Argoverse trajectory prediction.Vehicle routes follow Manhattan mobility, with straight movement probability 0.5 and left or right turns probability 0.25 each.Source: §VI · p. 9, A. Simulation Setups · p. 9
- The channel setup follows 3GPP V2X specifications and includes both line-of-sight and non-line-of-sight propagation.The model includes log-normal shadowing and Rayleigh small-scale fading.Source: A. Simulation Setups · p. 9
B. Model and Datasets
The evaluation uses CIFAR-10 image classification and Argoverse trajectory prediction, comparing FedPGT with schemes that differ in scheduling, resource allocation, and gradient transmission. It also tracks how estimated gradient compressibility changes during training.
C. Baseline Schemes
- The experiments compare FedPGT with four benchmark schemes across image-classification and trajectory-prediction tasks.Source: B. Model and Datasets · p. 10, C. Baseline Schemes · p. 10
B. Model and Datasets
- CIFAR-10 evaluation uses a six-convolution-layer network and a non-i.i.d. label-based partition in which each vehicle holds two classes.The dataset has 50,000 training images and 10,000 test images across 10 classes.Source: 1) CIFAR-10 · p. 10
- Argoverse evaluation uses LaneGCN to predict future positions over a 3-second horizon, with average displacement error (ADE) as the metric.The dataset contains over 300,000 sequences and is uniformly partitioned into 40 subsets.Source: 1) CIFAR-10 · p. 10
1) V2V-Enhanced FL (V2VFL) [8]:
- V2VFL dynamically schedules devices and uses vehicle-to-vehicle assistance, but only fully uploaded updates contribute to aggregation.Source: 1) V2V-Enhanced FL (V2VFL) [8] · p. 10
2) Vehicular Edge FL (VEFL) [7]:
- VEFL updates resource allocation dynamically according to instantaneous channel states while accounting for mobility and fast channel variations.Source: 2) Vehicular Edge FL (VEFL) [7] · p. 10
3) Joint Gradient Sparsification and Device Scheduling (JGSD) [10]:
- JGSD jointly schedules devices and sparsifies gradients, but fixes the sparsification degree at each round’s start.Source: 3) Joint Gradient Sparsification and… · p. 10
4) Static Scheduling Algorithm (SA) [13]:
- SA bases scheduling and resource allocation on initial channel states and vehicle locations, without mobility adaptation or sparsification.Source: 4) Static Scheduling Algorithm (SA) [13] · p. 10
D. Estimation of Gradient Compressibility Parameters
- The estimated compressibility exponent increases during training, indicating gradients become more compressible near convergence.Fewer dominant entries are then required to approximate the full gradient.Source: D. Estimation of Gradient… · pp. 10–11, Figure 5 · p. 10
E. Performance under Different Vehicle Speeds
Across vehicle speeds, participant counts, bandwidth conditions, and trajectory prediction, FedPGT is reported as robust under mobility and communication constraints. Its progressive transmission lets partially uploaded gradient entries contribute to aggregation.
E. Performance under Different Vehicle Speeds
- At high vehicle speeds, performance degrades across schemes, but FedPGT is most robust because partial updates can contribute despite interrupted transmissions.Dynamic resource allocation adapts to changing channels; progressive transmission makes partially transmitted updates usable.Source: E. Performance under Different Vehicle… · p. 11
F. Performance under Different Numbers of Vehicles
- As vehicle numbers grow, FedPGT and JGSD continue improving while full-upload schemes saturate when communication demand exceeds available resources.Partially transmitted gradient entries let more vehicles contribute under limited resources.Source: F. Performance under Different Numbers… · p. 11, Figure 11 · p. 11
G. Performance under Different Total Bandwidth
- Reducing total bandwidth from 30 MHz to 10 MHz degrades overall performance, while FedPGT remains the most robust in the low-bandwidth regime.The supplied figures report final accuracy and convergence performance under different bandwidth settings.Source: Figure 12 · p. 12, Figure 13 · p. 12, Figure 14 · p. 12
H. Evaluation on Argoverse Trajectory Prediction Dataset
- Under challenging Argoverse conditions—10 MHz bandwidth or vmax = 25 m/s—the performance gap between FedPGT and baselines becomes more significant.At vmax = 5 m/s and 20 MHz, all schemes are comparable and FedPGT has the lowest ADE.Source: Figure 15 · p. 12, Figure 16 · p. 12, Figure 17 · p. 12
VII. CONCLUSION
- FedPGT demonstrates robust learning under high mobility and limited communication resources across CIFAR-10 and Argoverse simulations.The conclusion attributes the approach to progressive gradient transmission and dynamic resource allocation.Source: §VII · p. 12, H. Evaluation on Argoverse Trajectory… · p. 12
APPENDIX A PROOF OF LEMMA 1
The appendix outlines proof steps for the gradient-ordering lemma and two theorems, using smoothness and Lyapunov-drift arguments.
APPENDIX A PROOF OF LEMMA 1
- The Lemma 1 proof begins by ordering gradient entries by descending magnitude.Source: Appendix A · p. 15
APPENDIX B PROOF OF THEOREM 1
- Theorem 1’s proof invokes L-smoothness, sets η ≤ 1/L, takes an expectation over stochastic sampling, and telescopes across rounds.Source: Appendix B · p. 15
APPENDIX C PROOF OF THEOREM 2
- Theorem 2’s proof defines a quadratic Lyapunov function and bounds single-round drift using queue and energy terms.It then sums the drift-plus-penalty bound over rounds.Source: Appendix C · pp. 15–16
- The proof also uses convexity and monotonic decrease of a function involving the compressibility exponent to apply Jensen’s inequality.Source: Appendix C · p. 16
APPENDIX D PROOF OF PROPOSITION 1
The appendix derives KKT conditions for P3 and uses them to establish Proposition 1.
APPENDIX D PROOF OF PROPOSITION 1
- The proof introduces the Lagrangian of P3 before deriving its KKT conditions.Source: Appendix D · p. 16
- The KKT argument uses nonnegative multipliers λz, ςn,z, νn, and χn,z to derive a condition for each vehicle and resource block.Source: Appendix D · p. 17
- For nonzero sn,z(t), the left side of condition (43) reaches its lower bound λz, completing the proposition’s proof.Source: Appendix D · p. 17
APPENDIX E PROOF OF PROPOSITION 3
The appendix proves Proposition 3 by separating optimal power-allocation cases according to ζn(t) and qn(t), using objective monotonicity and transmission-rate behavior.
APPENDIX E PROOF OF PROPOSITION 3
- For ζn(t) ≥ 0, the objective is nondecreasing in each pn,z(t), which determines the optimal-solution case.The passage does not include the resulting allocation expression.Source: Appendix E · p. 17
- When ζn(t) < 0 and qn(t) = 0, the objective decreases with achievable transmission rate, so the total power constraint is active.The resulting power allocation expression is not included.Source: Appendix E · p. 17
- The appendix states that the proposition is proved.Source: Appendix E · p. 17
- For ζn(t) < 0 and qn(t) > 0, the proof combines cases to give an optimal power allocation; n(t) denotes the RB subset assigned positive power.The allocation expression itself is not included.Source: Appendix E · p. 17