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Federated Learning in the Sky: Joint Power Allocation and Scheduling with UAV Swarms
Tengchan Zeng, Omid Semiari, Mohammad Mozaffari, Mingzhe Chen, Walid Saad, Mehdi Bennis
TL;DR
The paper addresses how UAV swarms can perform learning despite unreliable connections to ground base stations and wireless effects that influence FL convergence. It develops a distributed FL framework with convergence analysis and jointly designs power allocation and scheduling under energy and control-delay constraints. Simulations validate the analysis and report up to a 35% reduction in convergence rounds compared with a baseline design.
Problem
Unreliable UAV-to-ground-BS connectivity makes centralized ML challenging for large data volumes, while wireless delay and antenna deviations affect FL convergence.
Method
The paper implements distributed FL with follower-side local training and leader-side aggregation, analyzes wireless impacts on convergence, and jointly designs power allocation and scheduling under energy and delay constraints.
Results
35%: the joint design reduces the FL convergence round by as much as 35% compared with the baseline system without joint design.
Takeaways & Limitations
The convergence analysis characterizes how uplink and downlink delay requirements interplay with FL performance, supporting wireless-aware UAV-swarm FL design.
Abstract
from arXiv · showhide
Unmanned aerial vehicle (UAV) swarms must exploit machine learning (ML) in order to execute various tasks ranging from coordinated trajectory planning to cooperative target recognition. However, due to the lack of continuous connections between the UAV swarm and ground base stations (BSs), using centralized ML will be challenging, particularly when dealing with a large volume of data. In this paper, a novel framework is proposed to implement distributed federated learning (FL) algorithms within a UAV swarm that consists of a leading UAV and several following UAVs. Each following UAV trains a local FL model based on its collected data and then sends this trained local model to the leading UAV who will aggregate the received models, generate a global FL model, and transmit it to followers over the intra-swarm network. To identify how wireless factors, like fading, transmission delay, and UAV antenna angle deviations resulting from wind and mechanical vibrations, impact the performance of FL, a rigorous convergence analysis for FL is performed. Then, a joint power allocation and scheduling design is proposed to optimize the convergence rate of FL while taking into account the energy consumption during convergence and the delay requirement imposed by the swarm's control system. Simulation results validate the effectiveness of the FL convergence analysis and show that the joint design strategy can reduce the number of communication rounds needed for convergence by as much as 35% compared with the baseline design.
I. INTRODUCTION
The paper proposes distributed federated learning for UAV swarms because unreliable UAV-to-ground-BS connectivity makes centralized ML difficult for large data volumes. It analyzes wireless effects on FL convergence and jointly optimizes power allocation and scheduling under energy and control-system delay constraints.
- Distributed FL lets UAVs train on local data and share model parameters without sending raw data to centralized base stations.
- Wireless transmission delay and antenna-angle uncertainty can affect FL convergence and task consensus in mobile UAV swarms.
- The paper formulates joint power allocation and scheduling to reduce the FL convergence round while constraining learning, communication, and flight energy.
- The design also incorporates the control system’s delay constraint to help guarantee UAV-swarm stability.
- 35%: the joint design reduces convergence rounds by as much as 35% versus baselines without joint design.
II. SYSTEM MODEL
The system model is a wirelessly connected UAV swarm with one leader and multiple followers that collect data and perform FL for swarm tasks. Followers train local models and send their learned-model parameters to the leader over the uplink.
- The swarm contains one leading UAV and a set of follower UAVs flying at the same altitude.
- Followers maintain target distance and speed relative to the leader while the swarm collects data and performs FL.
- Each follower trains a local FL model from collected data and sends its model parameters to the leader through the uplink.
A. Federated learning model
The FL model uses follower-specific datasets and iterative local-update, aggregation, and global-distribution rounds. Communication timing and energy consumption are incorporated because failed transmissions affect model updates and convergence.
- A. Federated learning model: Each follower’s collected samples consist of input vectors paired with single outputs, and its local model is parameterized by a vector w_i.
- A. Federated learning model: The global FL objective aggregates loss over all follower datasets, with the loss function depending on the application.
- A. Federated learning model: Each round sends a global model to followers, trains local models, returns local vectors to the leader, and aggregates them into the next global model.
- A. Federated learning model: Uplink and downlink transmissions receive separate time budgets within each communication round, and links missing their deadlines cannot contribute updated models.
- A. Federated learning model: The model accounts for UAV energy used in learning and communication, including leader-side processing and follower-side training.
B. Communication model
The communication model represents UAV links with directional antennas, fading, interference, bandwidth, transmit power, and delay. Random antenna-angle deviations caused by environmental and mechanical effects alter link gains and therefore transmission conditions.
- B. Communication model: Directional antennas are used to reduce interference from UAVs outside the swarm.
- B. Communication model: Wind, payload, and nonideal mechanical or control systems cause random antenna-angle deviations modeled as Gaussian variables.
- B. Communication model: The antenna aperture is modeled with a squared cosine function and approximated by a sectionalized expression.
- B. Communication model: Uplink transmissions use separate wireless resources to reduce mutual interference, with delay determined by bandwidth, transmit power, path loss, fading, and noise.
- B. Communication model: Downlink delay depends on the downlink bandwidth, leader transmit power, and the UAVs generating downlink interference.
C. Control model
The control model accounts for UAV motion energy and communication delay to support stable swarm operation while designing the wireless network for FL convergence.
- Control requirements: The control system requires downlink delay constraints to guarantee stable UAV-swarm operation.Followers combine sensor data with leader broadcasts to coordinate movement and maintain target spacing and speed.
- Energy model: Each UAV consumes energy to overcome gravity and air drag during constant-speed flight.The model derives minimum motion power from induced velocity, thrust, rotor properties, and air density, then adjusts it using power efficiency.
- Design objective: The wireless design must account for learning, communication, and flying energy so each UAV remains within its energy limitation.The optimization also incorporates the control system’s delay requirement while minimizing the FL convergence round.
A. FL convergence analysis
The FL convergence analysis models how successful uplink and downlink transmissions affect iterative global-model updates and the number of rounds needed to reach a target accuracy.
- FL update process: The leading UAV initializes and aggregates local models, while followers update their local models using gradient descent.The leader broadcasts the resulting global model for the next communication round.
- FL update process: FL convergence requires successful local-model updates through uplink and global-model updates through downlink within their respective delay budgets.The global update is conditioned on both transmission delays meeting the scheduled uplink and downlink limits.
- Convergence metric: The convergence round is the minimum number of communication rounds needed to achieve an expected loss gap no greater than ε.The analysis assumes a continuously differentiable objective and standard conditions for convergence.
- Theorem 1: Theorem 1 characterizes convergence through the probability that both uplink and downlink satisfy their delay requirements.Increasing these probabilities improves convergence speed by making successful FL updates more likely.
B. Problem formulation and solution concept
The paper formulates joint power-allocation and scheduling optimization to minimize FL convergence rounds under energy, reliability, and motion constraints, solving the resulting stochastic problem approximately.
- Problem formulation: The optimization jointly designs UAV transmit powers, leader power, scheduling, and flight speed to minimize the FL convergence round.Its constraints include energy budgets, communication reliability for swarm stability, scheduling bounds, and feasible speed.
- Problem formulation: The objective and constraints reduce to probability terms that are difficult to evaluate directly and do not form a convex optimization problem.The paper therefore uses sample average approximation to replace the probability terms with sample-based expressions.
- Solution concept: Indicator functions are replaced with modified sigmoid functions to smooth the sample-average reformulation.The smoothing parameter controls how quickly the approximation changes near the indicator threshold.
- Solution concept: The dual problem is handled with subgradients and iterative optimization over power, scheduling, and speed variables.A central unit computes a sub-optimal solution before the swarm begins training.
IV. SIMULATION RESULTS AND ANALYSIS
The simulations validate the convergence analysis, show that angle deviations slow FL convergence while bandwidth helps, and demonstrate gains from joint power allocation and scheduling.
- Theorem validation: Less than 5% difference separates Theorem 1 from simulation results for convergence rounds versus the difference threshold ε.A larger threshold requires fewer communication rounds because the convergence requirement is less stringent.
- Angle deviations: Increasing angle-deviation variance increases the communication rounds required for FL convergence.Greater misalignment reduces antenna-gain products, increases transmission delay, and lowers the probability of satisfying delay requirements.
- Bandwidth impact: Increasing uplink and downlink bandwidth reduces the communication rounds needed for FL convergence.Larger bandwidth improves the probability that both transmission directions meet their delay requirements.
- Joint-design comparison: 35% is the maximum convergence-round reduction achieved by joint design versus optimized scheduling with randomized power allocation at 1 MHz bandwidth.The joint design has fewer convergence rounds than the baselines under the same network setting.
V. CONCLUSIONS
The paper analyzes how wireless factors affect federated-learning convergence in UAV swarms and jointly designs power allocation and scheduling to improve convergence while satisfying control and energy constraints.
- The convergence analysis examines transmission delay and antenna-angle deviations as wireless factors affecting federated-learning convergence.
- The proposed joint power-allocation and scheduling policy optimizes federated-learning convergence while guaranteeing control-system stability and controlling energy consumption.
- Simulation results corroborate the convergence analysis and show the merits of the proposed joint design.
APPENDIX
The appendix establishes expected linear convergence under smoothness, strong convexity, and gradient-growth assumptions, then derives a communication-round bound for reaching a target loss difference while accounting for wireless update errors.
- The analysis assumes that F(w) is continuously differentiable, has a uniformly Lipschitz-continuous gradient, and is strongly convex.These properties provide the regularity conditions used in the convergence derivation.
- Transmission delays are incorporated into the global-model update, producing an error term that enters the convergence analysis.The global model is first represented without delay and then rewritten after accounting for delayed transmissions.
- The derivation bounds the loss gap through the expected squared update error and obtains a strong expected linear-convergence condition.The resulting recursion contracts the expected loss difference by a factor involving the convergence-rate parameter.
- The appendix further derives the number of communication rounds required to reach a target threshold E(F(w)−F(w∗)) ≤ ε.The bound follows from repeated contraction and is rounded because the convergence round must be integral.