FMore: An Incentive Scheme of Multi-dimensional Auction for Federated Learning in MEC

Rongfei Zeng; Shixun Zhang; Jiaqi Wang; Xiaowen Chu

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FMore: An Incentive Scheme of Multi-dimensional Auction for Federated Learning in MEC

Rongfei Zeng, Shixun Zhang, Jiaqi Wang, Xiaowen Chu

arXiv:2002.09699v1Feb 22, 2020cs.LGcs.GTstat.ML

TL;DR

Federated learning in MEC lacks suitable incentives for edge nodes that incur heterogeneous resource costs and may not participate voluntarily. FMore applies a lightweight multi-dimensional procurement auction with K winners, deriving node strategies and aggregator guidance. Simulations and real-world experiments report fewer training rounds or less training time alongside higher model accuracy.

Problem
Existing federated-learning incentive mechanisms do not directly address MEC's voluntary participation problem, dynamic multi-dimensional resources, and need to select K winners.
Method
FMore uses a multi-dimensional procurement auction with K winners, Nash equilibrium strategies for edge nodes, and expected utility guidance for the aggregator.
Results
FMore reduces training rounds by 51.3% on average in simulations and reduces real-world training time by 38.4% while increasing model accuracy by 44.9%.
Takeaways & Limitations
FMore provides a lightweight, incentive-compatible mechanism intended to attract high-quality, low-cost edge nodes and improve federated-learning performance.

Abstract

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Promising federated learning coupled with Mobile Edge Computing (MEC) is considered as one of the most promising solutions to the AI-driven service provision. Plenty of studies focus on federated learning from the performance and security aspects, but they neglect the incentive mechanism. In MEC, edge nodes would not like to voluntarily participate in learning, and they differ in the provision of multi-dimensional resources, both of which might deteriorate the performance of federated learning. Also, lightweight schemes appeal to edge nodes in MEC. These features require the incentive mechanism to be well designed for MEC. In this paper, we present an incentive mechanism FMore with multi-dimensional procurement auction of K winners. Our proposal FMore not only is lightweight and incentive compatible, but also encourages more high-quality edge nodes with low cost to participate in learning and eventually improve the performance of federated learning. We also present theoretical results of Nash equilibrium strategy to edge nodes and employ the expected utility theory to provide guidance to the aggregator. Both extensive simulations and real-world experiments demonstrate that the proposed scheme can effectively reduce the training rounds and drastically improve the model accuracy for challenging AI tasks.

I. INTRODUCTION

Federated learning in MEC needs an incentive mechanism because edge participation consumes heterogeneous resources and nodes may not participate voluntarily. FMore addresses this through a lightweight multi-dimensional auction that selects K winners and targets high-quality, low-cost participants.

Edge nodes may avoid federated learning because participation consumes battery, bandwidth, and computation resources without compensation.
Existing incentive mechanisms cannot be directly applied to federated learning in MEC.
Heterogeneous and dynamic multi-dimensional resources create a need to select more high-quality edge nodes while controlling cost.
FMore uses a multi-dimensional procurement auction in which the aggregator broadcasts criteria, collects resource-quality and payment bids, and selects K winners.
FMore derives Nash equilibrium strategies for edge nodes and uses expected utility theory to guide the aggregator's resource acquisition.
Simulations report 51.3% fewer training rounds and 28% higher accuracy, while real experiments report 44.9% higher accuracy and 38.4% less training time.

III. FMORE: THE PROPOSED INCENTIVE SCHEME

FMore integrates auction-based recruitment with federated learning by scoring multi-dimensional resource bids, selecting K winners, and assigning payments before local training and global aggregation. Its design emphasizes incentive compatibility and lightweight computation and communication.

FMore executes six steps per training round: bid ask, bid collection, winner determination, task assignment, local training, and global aggregation.
The aggregator broadcasts a scoring rule over resource quality and expected payment, with resources including data, computation capability, bandwidth, and CPU cycles.
A node's bid reflects available resources and a private cost parameter, under single-crossing conditions ensuring marginal cost increases with that parameter.
Individual rationality requires participating nodes to have nonnegative profit, π_i(q_i, p_i) ≥ 0.
The aggregator selects the K highest-scoring nodes and may use either first-price or second-price payments; this paper uses first-price auction.
Compared with RandFL, FMore adds one information-exchange round, while total communication cost is linear in N and optimal-strategy computation is linear.

B. A Walk-Through Example

A five-node example illustrates FMore's scoring and winner-selection process with training data and bandwidth as resource dimensions. In the first round, the aggregator ranks bids and selects three winners for local learning.

The example uses five nodes, two resource types, data sizes from 1000 to 5000, and bandwidth from 5Mb to 100Mb.
The scoring function is S(q, p) = min{α_1q_1, α_2q_2} − p, with α_1 and α_2 both set to 0.5 after min-max normalization.
In round one, the aggregator chooses A, D, and E as the three winners after sorting all submitted bids by score.
The first-price payments for the three winners are 0.175, 0.221, and 0.300.
Nodes can change bids between rounds because available resources and private cost estimates change, or because nodes trade resources.

C. Discussion

FMore is extended for scenarios where resources are stable and local datasets are small, because repeatedly selecting fixed low-data or inferior-quality nodes may harm federated learning. The ψ-FMore extension randomizes winner selection among ranked nodes to increase data diversity.

When local data are small and resources are stable, repeatedly selecting fixed nodes with inferior-quality resources may negatively affect federated-learning performance.
ψ-FMore adds nodes in descending score order with probability ψ until K winners are selected, while FMore is the special case ψ = 1.
The parameter ψ should balance model accuracy and training speed, because a small ψ may deteriorate ψ-FMore into classic RandFL.

IV. OPTIMAL STRATEGY AND UTILITY ANALYSIS

This section derives equilibrium strategies and utility properties for FMore, including how node number and winner number affect profits. It also establishes resource-selection, Pareto-efficiency, and incentive-compatibility results.

Optimal Strategy: FMore’s analysis derives Nash equilibrium strategies for edge nodes and uses expected utility theory to guide the aggregator’s resource acquisition.The strategy includes resource qualities and expected payments; the quality choice depends on the private cost parameter.
Nash Equilibrium: The unique Nash equilibrium is characterized for first-price auctions with one winner, two winners, and K winners.The one-winner result is extended to two winners and then generalized to K winners.
Utility Analysis: The expected profit of each edge node decreases with the total node number N and increases with the winner number K.More participating nodes intensify competition, while selecting more winners raises participator profit.
Multiple Participation: With identical private values, adding probability ψ to each node does not change winning probabilities; with heterogeneous values, ψ-FMore redistributes selection toward lower-score nodes.The paper states that this increased involvement improves federated-learning performance in extreme cases because of increased data diversity.
Resource Utility: For multi-dimensional resources, quality choices are independent of payment and can be computed by maximizing the scoring function minus cost.The aggregator can adjust scoring weights to obtain different resource proportions, with cost coefficients estimated from historical market data.
Mechanism Properties: FMore is Pareto efficient when the aggregator’s utility equals the scoring function and has an additive form, and it is incentive compatible.Declaring lower resource quality reduces the score and therefore negatively affects winning probability.

V. PERFORMANCE EVALUATION

FMore is evaluated through simulations and real-world experiments to assess performance with many edge nodes and dynamic multidimensional resources.

The evaluation combines a large-scale smart simulator with a realistic deployment involving dynamic multidimensional resources.The simulator analyzes many edge nodes, while the real-world experiments assess performance in a realistic scenario.

A. Setup

The setup evaluates FMore against federated-learning baselines across four datasets, multiple neural models, non-IID data, and simulated or realistic MEC resources.

Four datasets—MNIST-O, MNIST-F, CIFAR-10, and HPNews—are evaluated with CNN and LSTM models under non-IID data distributions.FMore is compared with RandFL and FixedFL.
The simulator uses N = 100 participators and selects K = 20 winners per training round.Its resources are data size q1 and data-category proportion q2, with scores S(q1, q2, p) = αq1q2 −p.
The realistic cluster contains one aggregator and 31 nodes connected by a switch, with computing power, bandwidth, and data size as resources.The deployment uses a three-dimensional scoring function with coefficients 0.4, 0.3, and 0.3.
Simulation results are averaged over five experiments for both simulations and real-world experiments.

B. Simulations

Simulations show that FMore improves model accuracy and training efficiency relative to RandFL and FixFL, especially for challenging tasks. Varying N, K, and ψ reveals trade-offs among data diversity, accuracy, training rounds, and payment.

Simulation Goals: The simulations evaluate FMore’s performance improvement through model accuracy and training-time reduction across multiple learning tasks.The reported comparisons include CNN with MNIST-F and LSTM with HPNews.
Model Accuracy and Loss: FMore achieves higher model accuracy than RandFL and FixFL after 20 training rounds, with larger gaps for complicated models and challenging tasks.For LSTM, FMore reaches 60.4% accuracy at round 20, compared with 40.6% for FixFL.
Impacts of Parameter N: 28% fewer training rounds are needed to reach 84% accuracy when N increases from 50 to 100.Larger N improves data diversity, selection opportunities, accuracy, and training speed, while N = 200 already satisfies data-diversity needs.
Impacts of Parameter K: Increasing K from 5 to 25 reduces the rounds needed to reach 86% accuracy from 20 to 15.Larger K supplies more data and may improve accuracy, but it also increases winner payments and reduces winner scores.
Impacts of Parameter ψ: With ψ = 0.8, approximately 66.6% of selected nodes are among the top 30 scores, whereas ψ = 0.2 approaches RandFL.ψ-FMore performs better than FMore in small-datasize scenarios requiring greater data diversity.

C. Real-world Experiments

Real-world experiments show that FMore improves accuracy and reduces training time relative to RandFL. The experiments report these gains for challenging learning tasks, including CIFAR-10 and LSTM.

Accuracy Improvement: FMore reaches 59.9% CIFAR-10 accuracy after 20 rounds and improves accuracy by 44.9% compared with RandFL.Similar accuracy improvement is also reported for the LSTM model.
Evaluation Scope: The real-world evaluation examines accuracy, score distributions, and training speed and payment as functions of system parameters.The referenced figures cover score distribution and the effects of parameter K on training speed and payment.
Training-Time Reduction: FMore reduces the total CIFAR-10 training time for 20 rounds by 38.4%, to 1119.3 seconds.For reaching 50% CIFAR-10 accuracy, RandFL requires almost 17 rounds.

A. Mobile Edge Computing

Prior federated-learning research emphasizes performance, security, and privacy, while incentive mechanisms remain necessary for realistic MEC participation. FMore addresses this gap with a lightweight multi-dimensional procurement auction that selects K winners and targets efficient participation.

Research background: Federated-learning studies have primarily focused on performance improvement, security, and privacy rather than incentives.
Research gap: Voluntary participation assumptions fail in MEC because edge nodes consume battery, bandwidth, and computation resources during learning.
Research gap: Resource heterogeneity, multidimensional dynamic supplies, and selecting K winners require an incentive scheme tailored to MEC.
FMore: FMore uses a multi-dimensional procurement auction to select K winners and motivate high-quality edge nodes with low cost to participate.
FMore: FMore is lightweight and incentive compatible, with negligible computational overhead and communication costs in realistic deployment.
Evaluation: FMore reduces training rounds and improves accuracy in simulations and real-world experiments, including 51.3% fewer rounds and 44.9% higher accuracy in reported settings.The reported simulation result concerns the LSTM model, while the real-world result uses 32 nodes in a Linux HPC cluster.

APPENDIX

The appendix derives edge-node equilibrium bidding strategies and formulates the aggregator’s resource-selection problem using expected utility and a cost constraint.

Equilibrium analysis: When all nodes share the same private cost parameter θ, their scores and selection probabilities are identical.Selecting K nodes from N gives each node selection probability K/N, independent of ψ.
Equilibrium analysis: A Nash equilibrium strategy is shown by comparing it with an alternative bid that maximizes score minus cost and adjusts payment accordingly.
Aggregator optimization: The aggregator solves an expected-utility optimization problem under a cost constraint, using estimated coefficients ˜β_i and budget c0.The Lagrange multiplier method is used to compute the optimization solution and identify the aggregator’s optimal choices.