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Towards Federated Learning in UAV-Enabled Internet of Vehicles: A Multi-Dimensional Contract-Matching Approach

Wei Yang Bryan Lim, Jianqiang Huang, Zehui Xiong, Jiawen Kang, Dusit Niyato, Xian-Sheng Hua, Cyril Leung, Chunyan Miao

arXiv:2004.03877v1eess.SPcs.NI

TL;DR

The paper addresses privacy and incentive challenges in collaborative UAV services for IoV applications. It combines federated learning with a multi-dimensional contract and Gale-Shapley matching, and simulations validate truthful reporting, efficient matching, and model-owner profit maximization.

  • Problem

    Stringent data-privacy regulations impede raw-data sharing among independent DaaS providers, while information asymmetry creates incentive mismatches between UAVs and model owners.

  • Method

    Federated learning supports privacy-preserving collaboration, while a multi-dimensional self-revealing contract models heterogeneous UAV costs and Gale-Shapley matching assigns UAVs to subregions.

  • Results

    Simulations validate the contract’s incentive compatibility and matching efficiency, with the lowest marginal-cost UAV matched to each subregion.

  • Takeaways & Limitations

    The design supports privacy-preserving collaborative learning for IoV applications while guaranteeing model-owner profit maximization amid information asymmetry.

Abstract

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Coupled with the rise of Deep Learning, the wealth of data and enhanced computation capabilities of Internet of Vehicles (IoV) components enable effective Artificial Intelligence (AI) based models to be built. Beyond ground data sources, Unmanned Aerial Vehicles (UAVs) based service providers for data collection and AI model training, i.e., Drones-as-a-Service, is increasingly popular in recent years. However, the stringent regulations governing data privacy potentially impedes data sharing across independently owned UAVs. To this end, we propose the adoption of a Federated Learning (FL) based approach to enable privacy-preserving collaborative Machine Learning across a federation of independent DaaS providers for the development of IoV applications, e.g., for traffic prediction and car park occupancy management. Given the information asymmetry and incentive mismatches between the UAVs and model owners, we leverage on the self-revealing properties of a multi-dimensional contract to ensure truthful reporting of the UAV types, while accounting for the multiple sources of heterogeneity, e.g., in sensing, computation, and transmission costs. Then, we adopt the Gale-Shapley algorithm to match the lowest cost UAV to each subregion. The simulation results validate the incentive compatibility of our contract design, and shows the efficiency of our matching, thus guaranteeing profit maximization for the model owner amid information asymmetry.

I. INTRODUCTION

The paper combines UAV-enabled federated learning with multi-dimensional contract matching to support privacy-preserving IoV applications despite heterogeneous UAV costs and incentive misalignment.

  • Motivation: DaaS providers offer on-demand data collection and model training, while IoV applications use diverse sensing sources such as vehicular sensors, IoT devices, and RSUs.Applications include traffic prediction, traffic management, route planning, and parking-occupancy analysis.
  • Motivation: Federated Learning enables independent DaaS providers to collaborate without exchanging potentially sensitive raw data.UAVs train locally and transmit only updated model parameters for global aggregation.
  • Contributions: The proposed scheme aids time-sensitive IoV sensing and training, preserves UAV-collected data privacy, and reduces communication by transmitting model parameters instead of raw data.It is presented as an FL-based sensing and collaborative learning scheme for Intelligent Transport Systems.
  • Incentive mechanism: Information asymmetry lets UAVs misreport their types, conflicting with model owners’ goal of selecting the lowest-cost UAVs across sensing, transmission, and computation dimensions.The design addresses this incentive mismatch through contract theory’s self-revealing properties.
  • Incentive mechanism: A multi-dimensional contract accounts for sensing, computation, transmission, and traversal heterogeneity, while Gale-Shapley matching assigns an optimal UAV to each subregion.The system divides regions into smaller subregions because of UAV energy constraints and task time limits.
  • Contributions: Compared with prior UAV-subregion matching without truthful-reporting mechanisms, the paper combines self-revealing contracts with matching and targets the most optimal UAV for each sensing subregion.The formulation is intended to extend to specific FL-based IoV applications while accounting for multiple UAV-type heterogeneities.

III. SYSTEM MODEL AND PROBLEM FORMULATION

The system divides a target sensing region into subregions and assigns UAVs to collect data under sensing, traversal, and coverage constraints. Its two stages are multi-dimensional contract design and UAV–subregion assignment.

  • System model: The model owner partitions the target sensing region into N subregions and selects one UAV to cover each subregion.Subregions are represented as smaller graphs containing sensing nodes.
  • System model: The formulation assumes nodes are inter-accessible, so every pair of distinct nodes within a subregion has finite Euclidean distance.The distance is measured between node locations in R^3.
  • System model: UAV bases surround the sensing region, with J ≥ N and one UAV initially associated with each base.The model can be extended to require UAV swarms for sensing in each subregion.
  • System stages: The system first designs contracts using private sensing, computation, traversal, and transmission cost types, then assigns UAVs to subregions according to reported preferences.The contract stage selects feasible low-cost UAVs, while the assignment stage uses UAV rankings of subregions.
  • A. UAV Sensing Model: UAV sensing is modeled through node-coverage assignments, where a_ij,n indicates whether the UAV traverses a node-to-node segment.Coverage proportion θ_j,n satisfies 0 ≤ θ_j,n ≤ 1.
  • A. UAV Sensing Model: The total UAV travel includes sensing distance between assigned nodes and traversal distance to and from its base.The UAV travels at average velocity v_j and uses a fixed propulsion-power model.
  • A. UAV Sensing Model: Sensing and traversal costs depend on coverage and travel requirements, with traversal ordering varying across subregions while sensing-cost ordering remains fixed.Longer distances can increase traversal cost, whereas sensing-cost variation follows the sensing area.

B. UAV Computation Model

After sensing, each selected UAV trains the model locally and participates in federated aggregation over K global iterations. Computation cost depends on data volume, required local accuracy, hardware parameters, and processing capacity.

  • B. UAV Computation Model: Each selected UAV returns to its base and performs local FL training over K global iterations to minimize the global loss F_K(w).Each iteration includes local computation, wireless transmission of updates, and global parameter aggregation.
  • B. UAV Computation Model: A UAV trains the received global model locally, transmits its parameter update, and receives the aggregated global model for the next iteration.The aggregation combines updates derived from the N subregions.
  • B. UAV Computation Model: Local training minimizes an L-Lipschitz, γ-strongly convex loss up to target accuracy A*, without requiring local optimality.A larger A* represents greater deviation from the optimum and can reduce local computation duration.
  • B. UAV Computation Model: The FL process completes after K = a^(1−A*) global iterations, with a determined by the loss-function parameters and ξ.The model constrains 0 ≤ ξ ≤ γ/L.
  • B. UAV Computation Model: Computation energy is parameterized by effective switched capacitance, cycles per bit, collected samples, local-iteration requirements, and CPU frequency.The computation-cost coefficient β_j increases with energy cost per additional node coverage.
  • B. UAV Computation Model: Computation-cost ordering across UAV types is retained across subregions, although the number of collected data samples varies by subregion.This preserves a consistent ordering for computation costs in the model.

C. UAV Transmission Model

The transmission model accounts for wireless upload of fixed-size model updates, while the utility model links coverage, rewards, energy costs, and model-owner profit. The contract stage then enforces IR and IC constraints.

  • C. UAV Transmission Model: After local computation, selected UAVs wirelessly transmit model updates to the model owner.The achievable rate is modeled as transmit power multiplied by a scaling factor covering bandwidth and channel gain.
  • C. UAV Transmission Model: The model-upload size remains constant regardless of global-iteration count or collected-data quantity.Transmission duration and energy therefore depend on the fixed update size and communication parameters.
  • D. UAV and Model Owner Utility Modeling: A UAV’s utility combines its contractual reward with the unit energy cost incurred while covering a subregion.The reward term is denoted by the contractual reward, and φ is the unit energy cost.
  • D. UAV and Model Owner Utility Modeling: Aggregate model performance is represented as a concave function of data collected by the selected UAVs across all subregions.The formulation uses average node coverage across regions, analogous to Federated Averaging.
  • D. UAV and Model Owner Utility Modeling: The model owner’s total profit combines converted model performance with contractual reward expenses for selected UAVs.σ converts model performance into profits, while R_n,j* denotes each selected UAV’s reward expense.
  • D. UAV and Model Owner Utility Modeling: The next contract design must satisfy Individual Rationality and Incentive Compatibility simultaneously.These constraints ensure non-negative utility for truthful participation and prevent choosing contracts intended for other types.

A. Contract Condition Analysis

The contract model handles private, heterogeneous UAV costs by reducing a non-convex multi-dimensional problem to a tractable ordered formulation. Fixed compensation accounts for traversal and transmission costs before IR and IC are imposed.

  • Contract formulation: Sensing, traversal, computation, and transmission costs are private information, motivating a self-revealing multi-dimensional contract mechanism.The mechanism is designed to induce truthful revelation of UAV types.
  • Contract formulation: UAV types are indexed across X traversal, Y sensing, Z computation, and Q transmission cost dimensions.A type-(x, y, z, q) UAV is represented by one index from each ordered cost dimension.
  • Contract formulation: The mechanism orders UAVs by an auxiliary one-dimensional type based on marginal node-coverage cost, then derives coverage–reward bundles for each subregion.This reduction follows the multi-dimensional contract approach described in the paper.
  • Contract formulation: Traversal and transmission costs are compensated through a fixed reward component because they do not depend on the number of covered nodes.The final contract adds fixed compensation ˆR to the coverage-linked reward.
  • Contract conditions: A feasible contract must satisfy IR, requiring non-negative utility for a UAV choosing its designated item.IR is defined for each type-(y,z) UAV selecting contract item ω_y,z.
  • Contract conditions: IC requires each UAV to maximize utility by selecting the contract item designed for its own type rather than another type.This gives the UAV no incentive to choose contracts intended for other types.
  • Contract formulation: The original optimization contains YZ individual-rationality constraints and YZ(YZ−1) incentive-compatibility constraints, making it non-convex.The formulation therefore converts the contract into a single-dimensional problem.

B. Conversion Into A Single-Dimensional Contract

The multi-dimensional contract is transformed by ordering UAV types according to marginal node-coverage costs. Feasibility then reduces to monotonicity, individual rationality, and adjacent pairwise incentive-compatibility conditions.

  • Marginal node-coverage cost captures the additional sensing and computation expenses incurred when a UAV covers another node.
  • UAV types are sorted in non-decreasing order of marginal node-coverage cost, producing an auxiliary single-dimensional ordering.
  • For any feasible contract, lower coverage corresponds exactly to lower contractual reward under the established type ordering.
  • Monotonicity requires that a UAV with higher marginal cost receive no greater node coverage than a lower-cost type.
  • Feasibility can be checked through one minimum-utility UAV IR constraint and adjacent PIC constraints instead of all original IR and IC constraints.
  • The sufficient conditions require non-negative utility for the highest-cost type and bounded rewards satisfying adjacent pairwise incentive compatibility.

D. Contract Optimality

The optimal contract assigns rewards that satisfy feasibility while minimizing payments, and it identifies the lowest marginal-cost UAV as optimal for each subregion. Fixed traversal compensation preserves self-revelation but may require calibration when participation fails.

  • Adding fixed traversal and transmission compensation preserves incentive compatibility because those terms are structurally separate from marginal sensing and computation costs.
  • For known feasible coverage, optimal rewards are defined recursively from the highest-cost type toward the selected UAV type.
  • The model owner chooses the lowest rewards satisfying individual rationality and incentive compatibility to maximize profit.
  • If no UAV responds in a subregion, the fixed compensation can be calibrated upward, although some individual-rationality constraints may otherwise fail.
  • The optimal UAV for each subregion is the type-1 UAV with the lowest marginal node-coverage cost.
  • A closed-form coverage-reward pair is used when monotonicity holds; otherwise, Bunching and Ironing adjusts the result to satisfy it.

V. UAV-SUBREGION ASSIGNMENT

Because every subregion prefers the lowest UAV type, the paper formulates UAV selection as a two-sided matching problem to assign optimal UAVs efficiently.

  • The Gale-Shapley algorithm is needed because all subregions prefer type-1 UAVs, creating competition for the same optimal providers.

A. Matching Rules

The matching rules define preferences, proposals, rejections, and reward calibration for assigning UAVs to subregions. Iterative preference updates resolve ties among UAVs with identical marginal costs.

  • Matching Rules: A matching maps each UAV to one subregion or to no assignment, using subregion and UAV preference sets.
  • Matching Rules: Eligible UAVs announce their types, after which each subregion proposes to its most-preferred UAV.
  • Matching Rules: The Gale-Shapley procedure initializes feasible preferences, iteratively matches subregions and UAVs, and applies reward adjustments while ties remain.
  • Matching Rules: A UAV rejects a subregion when a better matching candidate exists; otherwise, the subregion remains a matching candidate.
  • Matching Rules: When multiple UAVs share the same marginal-cost preference, traversal and transmission compensation is reduced and preferences are renewed for another matching iteration.

B. Matching Implementation and Algorithm

The implementation filters UAVs by task feasibility, constructs preferences, and applies Gale-Shapley matching until every feasible subregion is assigned or no candidates remain. The contract ensures truthful type reporting, while matching assigns one optimal UAV to each subregion.

  • Initialization: The model owner announces subregions and time constraints, then admits only UAVs able to satisfy task requirements.A completion threshold such as 80% route coverage can determine which UAVs announce their types.
  • Initialization: The algorithm initializes unmatched subregions and their preference sets before iterative matching begins.R contains unmatched subregions, while P_n records subregion preferences.
  • Iterative Matching: Each subregion proposes to its most preferred feasible UAV using the corresponding node-coverage and contract-reward pair.If multiple optimal UAVs are tied, rewards are calibrated downward until a one-to-one match is obtained.
  • Iterative Matching: Rejected subregions return to the proposal pool, and preference lists are updated until all subregions are matched or exhausted.The procedure follows the Gale-Shapley algorithm and removes rejected UAVs from the relevant preference lists.
  • Properties: The stable matching assigns one optimal UAV to each region, while the contract’s self-revealing properties ensure truthful type reporting.The paper links Gale-Shapley stability and optimality to the assignment outcome.

VI. PERFORMANCE EVALUATION

The evaluation studies contract optimality using progressively broader UAV and subregion settings. Results support monotonic contract behavior, incentive compatibility, and the model owner’s preference for the lowest-cost feasible UAV.

  • Evaluation Setup: The evaluation examines a single subregion with six UAVs, then matching scenarios involving multiple UAVs and subregions.Simulation parameters are drawn from prior UAV and federated-learning optimization studies.
  • Contract Optimality: Type-1 UAV receives node coverage 1 and reward 35, whereas type-6 receives coverage close to 0.4 and reward 20.The comparison holds traversal and transmission cost types constant and assumes all UAVs meet time constraints.
  • Contract Optimality: Higher marginal node-coverage cost corresponds to lower optimal coverage and contract reward, validating the contract’s monotonicity condition.Figures 2 and 3 illustrate this relationship across auxiliary UAV types.
  • Incentive Compatibility: Type-6 UAV obtains negative utility when misreporting as any lower-cost type, validating incentive compatibility and truthful reporting.The contract gives each UAV its highest utility when it reports its type truthfully.
  • Profit Maximization: The model owner’s profit is highest when matched with the UAV having the lowest marginal cost of node coverage.This confirms the model owner’s stated preference among UAVs that can complete the task.

B. UAV-Subregion Preference Analysis

UAV and subregion preferences are determined by marginal coverage costs and traversal costs, then used to produce stable assignments. The simulations show that the mechanism selects efficient matches and remains consistent across heterogeneous subregions.

  • Preference Analysis: Subregions rank UAVs by ascending marginal node-coverage cost, with ties between types 1 and 2 and between types 4 and 5.All three subregions share the preference order (1, 2, 3, 4, 5).
  • Preference Analysis: UAV preferences depend on traversal costs, producing different rankings of subregions for different UAVs.UAVs 1 and 2 prefer (2, 3, 1) and (1, 3, 2), respectively.
  • Preference Analysis: UAV 1 matches region 2 and UAV 2 matches region 1, while UAV 5 prefers only its closest region because other assignments may yield negative profits.The first two assignments result from matching UAV and subregion preferences.
  • Preference Analysis: Downward reward calibration resolves ties for subregion 3 and leaves UAV 4 as the sole remaining choice.The calibration follows the proposed reward rule until one UAV remains.
  • Matching Outcomes: The matching mechanism assigns lower-cost UAVs to nearby subregions, validating the efficiency of matching the best available UAV.The resulting assignment reflects both UAV and subregion preferences.
  • Matching-Based Assignment: With heterogeneous data quantities and sensing areas, matching remains unchanged because preference rankings and UAV-type ordering remain constant.The preserved ordering supports contract monotonicity across subregions.
  • Matching-Based Assignment: When UAVs outnumber subregions, UAV 7 replaces UAV 1 on subregion 6, UAVs 1 and 2 receive lower-ranked choices, and UAV 6 is unassigned.UAV 7 has the lowest marginal node-coverage cost among the available UAVs.
  • Conclusion: The simulations validate truthful reporting, lowest-cost matching, and model-owner profit maximization.These outcomes summarize the claimed efficiency of the incentive and matching design.
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