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Optimal Auction For Edge Computing Resource Management in Mobile Blockchain Networks: A Deep Learning Approach
Nguyen Cong Luong, Zehui Xiong, Ping Wang, Dusit Niyato
TL;DR
Mobile blockchain mining is constrained by the computing and energy demands placed on mobile devices, while edge-resource allocation must maximize ECSP revenue and preserve incentive compatibility and individual rationality. The paper develops a deep-learning optimal auction derived from an analytical solution, and simulations report quick convergence with higher revenue than the SPA baseline.
Problem
Mobile blockchain mining consumes substantial computing and energy resources, creating an open need for edge-resource allocation that maximizes ECSP revenue while ensuring incentive compatibility and individual rationality.
Method
The paper constructs a neural-network auction architecture from an analytical optimal-auction solution and trains it on miners’ valuations to optimize expected negated ECSP revenue.
Results
For N = 15 and ci ∼U[0.2; 0.5] with κ = 1, SPA revenue is 2.8966 while DL-based auction revenue is 3.1460.
Takeaways & Limitations
The proposed deep-learning auction quickly converges and achieves significantly higher ECSP revenue than the baseline scheme in the reported simulations.
Abstract
from arXiv · showhide
Blockchain has recently been applied in many applications such as bitcoin, smart grid, and Internet of Things (IoT) as a public ledger of transactions. However, the use of blockchain in mobile environments is still limited because the mining process consumes too much computing and energy resources on mobile devices. Edge computing offered by the Edge Computing Service Provider can be adopted as a viable solution for offloading the mining tasks from the mobile devices, i.e., miners, in the mobile blockchain environment. However, a mechanism needs to be designed for edge resource allocation to maximize the revenue for the Edge Computing Service Provider and to ensure incentive compatibility and individual rationality is still open. In this paper, we develop an optimal auction based on deep learning for the edge resource allocation. Specifically, we construct a multi-layer neural network architecture based on an analytical solution of the optimal auction. The neural networks first perform monotone transformations of the miners' bids. Then, they calculate allocation and conditional payment rules for the miners. We use valuations of the miners as the data training to adjust parameters of the neural networks so as to optimize the loss function which is the expected, negated revenue of the Edge Computing Service Provider. We show the experimental results to confirm the benefits of using the deep learning for deriving the optimal auction for mobile blockchain with high revenue
I. INTRODUCTION
Mobile blockchain mining strains mobile devices, motivating edge offloading and an auction that allocates scarce resources while maximizing ECSP revenue and preserving incentive properties. The paper uses a deep-learning architecture derived from an analytical optimal-auction solution and reports faster convergence and higher revenue than traditional auctions.
- Mobile blockchain mining requires substantial computing power and energy, limiting deployment on mobile devices.
- Edge computing offloads miners’ mining tasks to an ECSP, but efficient allocation of limited edge resources remains unresolved.
- The paper applies deep learning to learn an optimal auction whose inputs are miners’ bids and whose outputs encode allocation and payments.
- The neural-network architecture is built from an analytical solution and trained to optimize the ECSP’s expected revenue.
- Simulation results show quick convergence and significantly higher ECSP revenue than traditional auction schemes.
III. SYSTEM MODEL AND PROBLEM FORMULATION
This section introduces the mobile blockchain mining process and the system model for allocating edge computing resources.
- The section presents the miners’ mining process, the mobile blockchain network model, and the edge resource allocation problem.
A. Blockchain Mining Process
Mobile blockchain mining confirms transactions by solving Proof-of-Work and reaching consensus, but its computing, time, and energy demands motivate edge offloading.
- Mining confirms transactions by solving a Proof-of-Work puzzle and propagating its solution to reach consensus.
- The first miner that successfully solves the puzzle and reaches consensus receives the mining reward.
- Because Proof-of-Work requires high computing power, time, and energy, the paper introduces edge computing to offload mining from mobile devices.
B. Edge Computing for Blockchain Mining
The system models one ECSP resource unit as a single-item auction among miners whose valuations depend on block size and initial computing capacity. The auction must maximize ECSP revenue while ensuring DSIC and IR.
- The model contains N mobile miners and one ECSP resource unit that can be assigned to only one miner.
- A miner’s valuation increases with block size and decreases with its initial computing capacity.
- The resource-allocation problem is formulated as a single-item auction in which miners bid for the ECSP’s resource unit.
- The ECSP must choose the winner and payment to maximize revenue while guaranteeing dominant-strategy incentive compatibility and individual rationality.
IV. OPTIMAL AUCTION USING DEEP LEARNING
The paper uses a neural-network architecture that learns monotone bid transformations and implements allocation and payment rules while preserving optimal-auction guarantees.
- Miner bids are first transformed monotonically, after which SPA-0 determines allocation and conditional payment rules.SPA-0 denotes the second-price auction with zero reserve price.
- For any strictly monotonically increasing transform functions, the resulting allocation and conditional payment mechanism is DSIC and IR.This theorem constrains the neural-network architecture so learned auctions retain these properties.
- The architecture implements allocation and conditional payment rules for an optimal auction that maximizes ECSP revenue while ensuring DSIC and IR.The network learns transform functions rather than fixing their functional form.
- The training objective is the expected negated ECSP revenue, which is equivalent to maximizing expected revenue.Algorithm 1 updates network parameters using stochastic gradient descent.
- The architecture and its allocation and payment components are illustrated in Figures 2 and 3.
A. Monotone Transform Functions
Each miner’s bid is mapped through a learned monotone transformation implemented as a two-layer feed-forward network.
- The transform function φ_i maps miner i’s input bid b_i to a transformed bid.
- Each φ_i uses K groups of J linear functions combined with min and max operators.The linear functions are parameterized by weights and biases.
- The network resembles an autoencoder: an encoder transforms bids into another representation and a decoder inverts that transform.
B. Allocation Rule
The allocation rule approximates SPA-0 by assigning the resource to the highest transformed bid, with softmax providing a differentiable implementation.
- The resource goes to the miner with the highest transformed bid when that bid exceeds zero; otherwise, it remains unassigned.
- The neural network maps transformed bids to assignment probabilities using a softmax function and a dummy input b_{N+1}=0.
- The parameter κ controls approximation quality: larger κ improves accuracy but can make allocation less smooth and harder to optimize.
C. Conditional Payment Rule
The conditional payment rule first computes the SPA-0 payment from competing transformed bids, then applies the inverse bid transformation.
- The conditional payment rule gives miner i a price conditional on winning and is implemented in two steps.It first computes SPA-0 payment p_i^0, then derives p_i using Theorem 1.
- SPA-0 payment p_i^0 is the maximum of the other miners’ transformed bids and zero.A ReLU unit implements this non-negative payment.
- The winner’s conditional payment is obtained by applying the inverse transform to the SPA-0 payment.
- The payment network combines linear, max-min, ReLU, inverse-transform, and min-max layers.
D. Neural Network Training
The training procedure uses miners’ valuation profiles as inputs and optimizes neural-network parameters to minimize the ECSP’s expected negated revenue. Valuations are generated from block sizes and initial computing capacities under specified distributional assumptions, and optimization uses SGD.
- Training data: Miners’ valuation profiles form the training data, sampled independently and identically from a known distribution.The training set consists of valuation profiles for the miners.
- Valuation model: Each miner’s valuation is its private value for one resource computing unit and is modeled as v_i = t_i/c_i.Here, t_i denotes block size and c_i denotes initial computing capacity.
- Valuation model: Block sizes and initial capacities are assumed independent and uniformly distributed, allowing the valuation distribution f_V(v) to be derived from f_T(t) and f_C(c).The capacity distribution is restricted to positive values through c_min > 0.
- Network outputs: The neural network outputs miner assignment probabilities and conditional payments through weight and bias parameters.The matrices w and β contain the network parameters.
- Optimization: Training minimizes the expected, negated ECSP revenue over the network parameters using a Stochastic Gradient Descent solver.The valuation profiles are the inputs, and the loss function is the expected, negated revenue function.
V. PERFORMANCE EVALUATION
The evaluation compares the DL-based auction with SPA across miner counts, capacity distributions, and approximation parameters. The proposed auction converges quickly and generally produces higher ECSP revenue, while revenue also depends on competition, capacity ranges, and κ.
- Experimental setup: The DL-based auction is implemented in TensorFlow and compared with SPA using a training set of 1000 valuation profiles.L2 regularization is used to bound weight parameters during training.
- Experimental setup: Experiments vary the number of miners, initial-capacity distributions, and approximation parameter κ across multiple scenarios.The evaluated miner counts are 10, 15, and 20.
- Revenue comparison: For N = 15, c_i ∼U[0.2; 0.5], and κ = 1, DL-based revenue is 3.1460 versus 2.8966 for SPA.The paper reports revenue improvements in the other evaluated scenarios as well.
- Revenue comparison: The DL-based auction converges quickly to a solution on par with the other schemes while achieving significantly higher revenue than SPA.The baseline scheme is represented by the black and cyan lines in the figures.
- Scenario effects: With c_i ∼U[0.2; 0.5] and κ = 1, ECSP revenue increases as the number of miners rises because stronger competition potentially motivates higher service prices.The reported consequence is increased ECSP revenue.
- Scenario effects: For 10 miners, c_i ∼U[0.2; 0.5] yields higher expected revenue than c_i ∼U[0.4; 0.7] because lower capacities produce higher bids under fixed block-size distributions.The paper attributes the revenue difference to bids being inversely proportional to initial capacity.
- Scenario effects: For N = 10 and c_i ∼U[0.2; 0.5], expected revenue is 2.7741 for κ = 1 and 2.6811 for κ = 2.Higher κ improves approximation accuracy but makes optimization harder and more complex, which may reduce expected revenue.
VI. CONCLUSIONS
The paper develops a deep-learning-based optimal auction for edge resource allocation in mobile blockchain networks. Simulations show rapid convergence and significantly higher ECSP revenue than the baseline, while future work remains for broader auction settings and architecture design.
- The proposed scheme develops an optimal auction based on deep learning for edge resource allocation in mobile blockchain networks.The neural-network architecture is based on an analytical solution.
- Miner valuations train the neural networks, whose parameters are adjusted to optimize the ECSP’s expected, negated revenue.The training design uses miners’ valuations as input data.
- The scheme quickly converges to a solution with significantly higher ECSP revenue than the baseline scheme.This result is reported from the simulation results.
- Future work should consider multiple edge computing resource units and optimal-auction architectures that do not rely on analytical characterization results.