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Incentive Design for Efficient Federated Learning in Mobile Networks: A Contract Theory Approach

Jiawen Kang, Zehui Xiong, Dusit Niyato, Han Yu, Ying-Chang Liang, Dong In Kim

arXiv:1905.07479v2cs.LGcs.GTcs.NI

TL;DR

Federated learning reduces privacy exposure by keeping raw data on mobile devices, but existing work often overlooks incentives for participation despite computation and communication costs. This paper applies contract theory to reward data quality and resource contributions under information asymmetry. Numerical results indicate that the mechanism attracts more high-quality data owners and supports efficient federated learning.

  • Problem

    Existing federated-learning studies largely optimize algorithm performance while overlooking incentives for self-interested mobile devices facing computation and communication costs.

  • Method

    The paper designs a contract-theory incentive mechanism that maps contributed resources to rewards and uses local-data quality as the contract-model type.

  • Results

    Numerical results indicate that the proposed scheme attracts more high-quality data owners and ensures more efficient federated learning.

  • Takeaways & Limitations

    Contract-based rewards can motivate high-quality local-data owners to join federated-learning processes.

Abstract

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To strengthen data privacy and security, federated learning as an emerging machine learning technique is proposed to enable large-scale nodes, e.g., mobile devices, to distributedly train and globally share models without revealing their local data. This technique can not only significantly improve privacy protection for mobile devices, but also ensure good performance of the trained results collectively. Currently, most the existing studies focus on optimizing federated learning algorithms to improve model training performance. However, incentive mechanisms to motivate the mobile devices to join model training have been largely overlooked. The mobile devices suffer from considerable overhead in terms of computation and communication during the federated model training process. Without well-designed incentive, self-interested mobile devices will be unwilling to join federated learning tasks, which hinders the adoption of federated learning. To bridge this gap, in this paper, we adopt the contract theory to design an effective incentive mechanism for simulating the mobile devices with high-quality (i.e., high-accuracy) data to participate in federated learning. Numerical results demonstrate that the proposed mechanism is efficient for federated learning with improved learning accuracy.

I. INTRODUCTION

Federated learning protects mobile-device data by sharing model updates rather than raw data, but participation incentives remain underdeveloped because training incurs resource costs and information asymmetry. The paper uses contract theory to reward higher-quality data and resource contributions, with experiments showing the mechanism outperforms existing approaches.

  • Motivation: Federated learning lets mobile devices jointly train a shared global model while sending local model updates instead of raw data.This decouples model training from centralized acquisition, storage, and training of user data.
  • Research gap: Existing studies emphasize learning performance, while often assuming mobile devices participate unconditionally despite computation and communication costs.The paper identifies this assumption as impractical for self-interested devices without economic compensation.
  • Approach: The paper designs a contract-theory incentive mechanism that maps contributed resources to appropriate rewards under information asymmetry.The mechanism targets mobile devices with high-quality data and motivates participation in federated model training.
  • Approach: Higher-type data owners with larger-accuracy and more reliable local data receive more rewards.The quality-related parameter of local data defines the contract-model type.
  • Evaluation: Real-world experiments on a digit classification dataset show that the proposed mechanism outperforms existing approaches.The paper presents numerical results after formulating and solving the contract-theory model.

II. PROBLEM FORMULATION

The formulation models federated learning as a monopoly market in which wireless infrastructures act as task publishers and mobile devices act as candidate data owners.

  • II. PROBLEM FORMULATION: A universal mobile network contains wireless infrastructures that publish federated learning tasks and mobile devices that serve as data-owner candidates.Mobile devices can generate application data and collect sensing data using their computation and communication capabilities.

A. Computation Model for Federated Learning

The computation model represents each data owner’s local training cost through dataset size, CPU cycle frequency, computation time, and energy consumption.

  • A. Computation Model for Federated Learning: Each data owner n participates with s_n local data samples and contributes CPU cycle frequency f_n for local model training.The task is modeled as a monopoly market with a task publisher and mobile devices indexed by N = {1, . . . , N}.
  • A. Computation Model for Federated Learning: Each data sample is assumed to have the same data size.This is an explicit modeling assumption in the computation model.
  • A. Computation Model for Federated Learning: The computation time of one local training iteration depends on the number of CPU cycles per sample, dataset size, and CPU frequency.The passage gives the relationship as c_n s_n / f_n.
  • A. Computation Model for Federated Learning: CPU energy consumption is modeled for one local iteration using the chipset’s effective capacitance parameter.The energy expression is attributed to prior work, and ζ is identified as the effective capacitance parameter.

B. Communication Model for Federated Learning

The communication model accounts for local-update iterations, computation and uplink transmission time, transmission rate, and energy consumption during each global iteration.

  • B. Communication Model for Federated Learning: A global iteration combines local model-update computation with uplink communication of each participating data owner’s update.The number of local update iterations depends on local data quality when global accuracy is fixed.
  • B. Communication Model for Federated Learning: TDMA time-sharing is used to model wireless transmission, with data-owner locations fixed during local-model-parameter transmission.The transmission rate is denoted by r_n.
  • B. Communication Model for Federated Learning: The transmission rate depends on bandwidth, transmission power, channel gain, and background noise.The model defines r_n = B ln(1 + ρ_n h_n / N_0).
  • B. Communication Model for Federated Learning: The model expresses transmission time and communication energy for sending a local model update of constant size σ.The update size has the same value for all data owners.
  • B. Communication Model for Federated Learning: Downlink time is treated as negligible compared with uplink time because downlink bandwidth is typically much larger.This assumption limits the communication model to the dominant uplink contribution.

C. Profit Function of the Task Publisher

The task publisher’s profit depends on local data quality, contributed computation resources, completion time, and reward costs. Higher-quality data and larger CPU frequency improve publisher profit, while rewards and budget constraints limit feasible contracts.

  • Data quality is modeled as each owner’s contract type, with higher types representing more accurate and reliable local data.The publisher knows the probability distribution of owner types but not each owner’s exact type.
  • The publisher offers type-specific resource-reward bundles (Rn(fn)), where fn is computation resource and Rn(fn) is the corresponding reward.More contributed computation resource accelerates local training and can yield higher rewards.
  • The publisher’s utility increases with training-time satisfaction and decreases with reward expenditure.Its satisfaction function depends on the total time of one global iteration, while lRn represents reward cost.
  • Higher data quality and larger CPU cycle frequency both improve the task publisher’s profit.Higher-type owners can increase publisher profit, although they also incur greater reward costs.
  • The publisher maximizes profit subject to nonnegative profit and contract feasibility constraints.The formulation requires UT P(Rn) ≥ 0 while accounting for resource, reward, and participation conditions.

D. Utility Function of Data Owners

The data owner’s utility equals its reward minus weighted energy consumption. Self-interested owners participate only when rewards offset their costs, and higher-type owners obtain larger utility from providing better-quality data.

  • A type-n data owner’s utility is defined as reward minus a weighted energy-consumption cost.The utility is UD(fn) = Rn − µEt, where µ weights energy consumption.
  • Data owners are self-interested and have zero utility when no reward is provided.Their utility therefore depends on whether the contract compensates participation costs.
  • Higher-type data owners have larger utility because they provide better-quality data.Owners also seek to minimize energy consumption during federated learning.

III. OPTIMAL CONTRACT DESIGNING

The optimal contract design enforces participation and truthful contract selection under information asymmetry, while optimizing computation resources and rewards within publisher constraints. The solution uses monotonicity, reduced incentive constraints, and concave optimization.

  • Contract constraints: Each contract must satisfy Individual Rationality and Incentive Compatibility so every data-owner type is properly motivated.IR ensures participation utility is nonnegative; IC ensures owners prefer contracts designed for their own types.
  • Contract constraints: Individual Rationality requires a data owner’s utility to be at least zero, while Incentive Compatibility requires choosing its own contract type.These constraints address participation and truthful self-selection under information asymmetry.
  • Contract structure: The contract is monotonic: higher data-owner types receive no lower computation resources or rewards.Lemma 1 states fn ≥ fm and Rn ≥ Rm if and only if θn ≥ θm for distinct types.
  • Contract structure: The IC conditions can be reduced to Local Downward Incentive Constraints, and satisfying type 1’s IR constraint ensures the other IR constraints hold.These lemmas simplify the original contract optimization problem.
  • Solution method: The relaxed optimization is solved without monotonicity first, then the solution is checked and adjusted if needed.For nonuniform type distributions, an infeasible sub-sequence replacing algorithm enforces the final monotonic resource requirement.
  • Solution method: The transformed objective is concave because the publisher’s utility has a negative second derivative, enabling convex-optimization tools to calculate optimal CPU cycles and incentives.The resulting solution yields optimal computation resource f*n and corresponding incentive R*n.

IV. NUMERICAL RESULTS

Numerical experiments on MNIST evaluate the incentive scheme’s effects on task-publisher profit and contract feasibility. The proposed contract model rewards high-quality participation and outperforms the compared Stackelberg game model in publisher profit.

  • Experimental Setup: MNIST experiments use one task publisher and 100 data owners, initially classified into 10 equally probable data-quality types.The dataset contains 60,000 training examples and 10,000 test examples.
  • Profit and Data Quality: Publisher profit decreases as the upper limit of local data accuracy falls from 98% to 78%.The paper attributes this decline to fewer high-type data owners and reports that low-quality data negatively affects publisher profit.
  • Contract Feasibility: Each data-owner type reaches maximum utility only with its designated contract item, while that item provides nonnegative utility.These observations validate incentive compatibility and individual rationality under information asymmetry.
  • Model Comparison: For a fixed number of data-owner types, the proposed contract model yields higher task-publisher profit than the Stackelberg game model.The paper explains this result by the monopolist publisher offering limited contract choices and extracting more profit.
  • Model Comparison: Increasing the total number of data-owner types increases task-publisher profit by providing more contract-item choices to high-type owners.The paper links these additional choices to more efficient federated learning.

V. CONCLUSIONS

The paper concludes that its contract theory-based incentive mechanism motivates high-quality data owners to participate in federated learning. Numerical results indicate improved efficiency while optimizing utilities for both task publishers and data owners.

  • Conclusion: The contract theory-based mechanism motivates data owners with high-quality local training data to join federated learning.The mechanism is designed to support efficient learning processes.
  • Conclusion: Numerical results indicate that the scheme attracts more high-quality data owners and optimizes utilities for task publishers and data owners.The paper identifies blockchain-based reliability of local model updates as future work.
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