# Joint Incentive Mechanism Design and Energy-Efficient Resource Allocation for Federated Learning in UAV-Assisted Internet of Vehicles

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## Abstract

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## 1. Introduction

- Edge computing capabilities: UAVs can serve as edge services for federated learning, performing computation and learning tasks locally. This reduces the need for extensive data transfers and minimizes latency. Edge computing on UAVs enhances the scalability and efficiency of federated learning in distributed environments.
- Communication efficiency and mobility enhancement: By processing model aggregation locally on UAVs, there is a significant reduction in the need to transmit large amounts of raw data to a central server. What is more, UAVs can cover a wide geographic area efficiently, which addresses the training challenges associated with the high dynamicity of vehicles in IoV.
- Privacy-preserving surveillance: Federated learning allows for model training on decentralized data, addressing privacy concerns. UAVs can collect data or models locally without transmitting sensitive information to a central server. Privacy-preserving techniques, such as differential privacy, can be integrated into federated learning to further protect individual privacy.
- Network resilience: UAVs can operate in areas with limited network infrastructure or during network failures. Federated learning’s decentralized nature makes it resilient to intermittent connectivity, aligning well with the mobility and varying connectivity conditions in the IoV.

- We propose a UAV-assisted FL framework in the IoV. Each UAV acts as a central server to provide the model aggregation or model parameter relay in the sky, which increases the reliability of FL under the uncertain and high-mobility conditions in the IoV network.
- We design a contract-based incentive mechanism between UAVs and UVs. UAVs make contracts to assist VUs in responding to task publishers’ service requests and participating in federated training. Moreover, the contract mechanism determines VUs’ contributed local data based on their specific types in the presence of information asymmetry. VUs can receive corresponding revenues according to their data contributions.
- We design an energy-efficient resource allocation algorithm to minimize total energy consumption in the training stage. According to the contract’s specific willingness and types, UAV manages VUs’ computing and communication resources to achieve energy-efficient federated training.

## 2. Literature Review

#### 2.1. Incentive Mechanism in FL

#### 2.2. Resources Allocation in FL

## 3. Proposed FL Framework in UAV-Assisted IoV

## 4. Incentive Mechanism for Contracts of Vehicles

#### 4.1. Contract Feasibility

**Definition**

**1.**

**Definition**

**2.**

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Lemma**

**3.**

**Proof.**

**Proof.**

#### 4.2. Optimal Contract

## 5. Contract-Based Energy-Efficient Resource Allocation for UAV-Assisted FL

#### 5.1. System Models

#### 5.1.1. Communication Model

#### 5.1.2. Computation Model

#### 5.1.3. Mobility Model

#### 5.2. Problem Formulation

#### 5.3. Solution of the Optimization Problem

#### 5.3.1. Solution to P2

#### 5.3.2. Solution to P3

**Theorem**

**1.**

**Proof.**

Algorithm 1 Bisection Method for Transmission Power Allocation Algorithm |

Input: Initial section $[{a}^{0},{b}^{0}]=[{G}_{j},{p}_{j}^{max}],$ maximum tolerance $\u03f5>0$,Set $f({p}_{j})={I}_{i}^{glob}$${\sum}_{j=1}^{J}{p}_{j}\frac{s}{B{log}_{2}(1+\frac{{p}_{j}{g}_{j}}{{N}_{0}})}$, $t=1$, $conv=0$ Output: ${G}_{j}\le {p}_{j}^{*}\le {p}_{j}^{max}$1: while $conv$ = 0 do2: ${p}_{j}^{t}=\frac{{a}^{t-1}+{b}^{t-1}}{2}$ 3: Compute ${f}^{\prime}({p}_{j}^{t})$ 4: if ${f}^{\prime}({p}_{j}^{t})=0$ then5: ${p}_{j}^{*}={p}_{j}^{t}$, set $conv=1$ 6: end if7: if ${f}^{\prime}({p}_{j}^{t})<0$ then8: Update the section to $[{a}^{t},{b}^{t}]=[{p}_{j}^{t},{b}^{t-1}]$ 9: if $|{b}^{t-1}-{p}_{j}^{t}|\le \u03f5$ then10: ${p}_{j}^{*}={p}_{j}^{t}$, set $conv=1$ 11: set $t=t+1$ 12: end if13: end if14: if ${f}^{\prime}({p}_{j}^{t})>0$ then15: Update the section to $[{a}^{t},{b}^{t}]=[{a}^{t-1},{p}_{j}^{t}]$ 16: if $|{p}_{j}^{t}-{a}^{t-1}|\le \u03f5$ then17: ${p}_{j}^{*}={p}_{j}^{t}$, set $conv=1$ 18: set $t=t+1$ 19: end if20: end if21: end while |

Algorithm 2 Iterative Algorithm for the Whole Optimization Problem |

Input: Initial ${\mathit{sol}}^{(\mathbf{0})}=({\mathit{f}}^{(\mathbf{0})},{\mathit{p}}^{(\mathbf{0})})$, $t=1$, $conv=0$, maximum tolerance ${\u03f5}_{0}>0$Output: Optimal ${\mathit{sol}}^{*}=({\mathit{f}}^{*},{\mathit{p}}^{*})$1: while $conv$ = 0 do2: Solve $\mathit{P}\mathbf{2}$ to obtain ${f}_{j}^{t}$ according to Equation (52) 3: Solve $\mathit{P}\mathbf{3}$ to obtain ${p}_{j}^{t}$ according to Algorithm 1 4: ${\mathit{sol}}^{(\mathit{t})}=({\mathit{f}}^{(\mathit{t})},{\mathit{p}}^{(\mathit{t})})$, and set $t=t+1$ 5: Check the convergence of $|{\mathit{sol}}^{(\mathit{t})}-{\mathit{sol}}^{(\mathit{t}-\mathit{1})}|$ 6: if $|{\mathit{sol}}^{(\mathit{t})}-{\mathit{sol}}^{(\mathit{t}-\mathit{1})}|\le {\u03f5}_{0}$ then7: ${\mathit{sol}}^{(*)}={\mathit{sol}}^{\left(\mathit{t}\right)}$, and set $conv=1$ 8: end if9: end while |

## 6. Experimental Evaluation

#### 6.1. Simulation Settings

#### 6.2. Contract Optimality

#### 6.3. Performance of the Resource Allocation

- DCM: DCM [40] is a resource allocation algorithm in mobile edge computing that aims at capturing the trade-off between learning efficiency and energy consumption. It optimizes CPU frequency, data volume, and total FL delay.
- Benchmark1: Compared with the proposed algorithm, the CPU frequency ${f}_{j}$ of the vehicle is directly set to ${f}_{j}^{max}$.
- Benchmark2: Compared with the proposed algorithm, the power ${p}_{j}$ of the vehicle is directly set to ${p}_{j}^{max}$.
- Benchmark3: Compared with the proposed algorithm, the data volume of vehicles is randomly allocated.

#### 6.4. Performance of Federated Learning

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## References

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**Figure 10.**The performance of federated learning. (

**a**) Accuracy on a representative VU and (

**b**) Loss on a representative VU.

Description | Symbol |
---|---|

Path loss between ${c}_{j}$ and UAV at timeslot t | ${g}_{j}\left(t\right)$ |

Transmission model size of ${c}_{j}$ | ${\omega}_{j}$ |

Transmission power of VU ${c}_{j}$ | ${p}_{j}$ |

CPU cycle frequency of ${c}_{j}$ | ${f}_{j}$ |

Communication delay | ${T}_{j}^{com}$ |

Communication energy consumption | ${E}_{j}^{com}$ |

Computation delay | ${T}_{j}^{train}$ |

Computation energy consumption | ${E}_{j}^{train}$ |

Total delay of ${c}_{j}$ | ${T}_{j}$ |

Total energy consumption of ${c}_{j}$ | ${E}_{j}$ |

Local model accuracy of ${c}_{j}$ | ${\eta}_{j}^{loc}$ |

Local training iterations of ${c}_{j}$ | ${I}_{j}^{loc}$ |

Global training iterations of | ${I}_{0}$ |

Sojourn time of ${c}_{j}$ under UAV ${s}_{i}$ | ${T}_{sojourn}^{i,j}$ |

The data quantity ${c}_{j}$ contributed to task publisher | ${q}_{j}$ |

The reward of ${c}_{j}$ | ${R}_{j}$ |

The willingness of ${c}_{j}$ to participate in training | ${\epsilon}_{j}$ |

The proportion of type-j VU | ${\rho}_{j}$ |

VU’s unit cost required for training | c |

The utility of task publisher | ${U}_{TP}$ |

The utility of ${c}_{j}$ | ${U}_{j}$ |

Parameters | Values |
---|---|

Average speed of VU (${\overline{v}}_{j}$) | [20–30] m/s |

Noise power (${N}_{0}$) | −174 dBm/Hz |

Total data size | 47 MB |

Bandwidth of each VU (B) | 180 kHz |

Transmitted model size (${\omega}_{j}$) | 0.05 Mbits |

Maximum transmission power (${p}_{j}^{max}$) | 20 dBm |

Maximum CPU frequency (${f}_{j}^{max}$) | 2 GHz |

Learning rate | 0.001 |

Batch size | 128 |

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## Share and Cite

**MDPI and ACS Style**

Lin, S.; Li, Y.; Han, Z.; Zhuang, B.; Ma, J.; Tianfield, H.
Joint Incentive Mechanism Design and Energy-Efficient Resource Allocation for Federated Learning in UAV-Assisted Internet of Vehicles. *Drones* **2024**, *8*, 82.
https://doi.org/10.3390/drones8030082

**AMA Style**

Lin S, Li Y, Han Z, Zhuang B, Ma J, Tianfield H.
Joint Incentive Mechanism Design and Energy-Efficient Resource Allocation for Federated Learning in UAV-Assisted Internet of Vehicles. *Drones*. 2024; 8(3):82.
https://doi.org/10.3390/drones8030082

**Chicago/Turabian Style**

Lin, Shangjing, Yueying Li, Zhibo Han, Bei Zhuang, Ji Ma, and Huaglory Tianfield.
2024. "Joint Incentive Mechanism Design and Energy-Efficient Resource Allocation for Federated Learning in UAV-Assisted Internet of Vehicles" *Drones* 8, no. 3: 82.
https://doi.org/10.3390/drones8030082