[Paper Review] A Fast Graph Neural Network-Based Method for Winner Determination in Multi-Unit Combinatorial Auctions

Mengyuan Lee, Seyyedali Hosseinalipour+3 more|arXiv (Cornell University)|Sep 29, 2020

Auction Theory and Applications43 references4 citations

TL;DR

This paper proposes a graph neural network (GNN)-based method to solve the winner determination problem (WDP) in multi-unit combinatorial auctions (CAs), modeling the problem as an augmented bipartite bid-item graph and using half-convolution GNNs to predict bid inclusion probabilities. The approach achieves near-optimal revenue with significantly lower computation time than CPLEX and demonstrates strong generalization across problem sizes and user-type distributions.

ABSTRACT

The combinatorial auction (CA) is an efficient mechanism for resource allocation in different fields, including cloud computing. It can obtain high economic efficiency and user flexibility by allowing bidders to submit bids for combinations of different items instead of only for individual items. However, the problem of allocating items among the bidders to maximize the auctioneers" revenue, i.e., the winner determination problem (WDP), is NP-complete to solve and inapproximable. Existing works for WDPs are generally based on mathematical optimization techniques and most of them focus on the single-unit WDP, where each item only has one unit. On the contrary, few works consider the multi-unit WDP in which each item may have multiple units. Given that the multi-unit WDP is more complicated but prevalent in cloud computing, we propose leveraging machine learning (ML) techniques to develop a novel low-complexity algorithm for solving this problem with negligible revenue loss. Specifically, we model the multi-unit WDP as an augmented bipartite bid-item graph and use a graph neural network (GNN) with half-convolution operations to learn the probability of each bid belonging to the optimal allocation. To improve the sample generation efficiency and decrease the number of needed labeled instances, we propose two different sample generation processes. We also develop two novel graph-based post-processing algorithms to transform the outputs of the GNN into feasible solutions. Through simulations on both synthetic instances and a specific virtual machine (VM) allocation problem in a cloud computing platform, we validate that our proposed method can approach optimal performance with low complexity and has good generalization ability in terms of problem size and user-type distribution.

Motivation & Objective

• To address the high computational complexity of the winner determination problem (WDP) in multi-unit combinatorial auctions (CAs), which is NP-complete and inapproximable.
• To develop a low-complexity machine learning solution that generalizes across varying problem sizes and user-type distributions.
• To reduce reliance on expensive labeled training data by proposing efficient sample generation processes for the WDP.
• To design novel graph-based post-processing algorithms that transform GNN outputs into feasible auction allocations.
• To validate the method’s performance on both synthetic instances and real-world virtual machine (VM) allocation in cloud computing.

Proposed method

• The multi-unit WDP is modeled as an augmented bipartite graph where bids and items are nodes, and edges represent bid-item inclusion with unit counts.
• A graph neural network (GNN) with half-convolution operations is used to learn a continuous probability map indicating the likelihood of each bid being in the optimal allocation.
• Two distinct sample generation processes are introduced to improve data efficiency and reduce the number of required labeled training instances.
• Two novel graph-based post-processing algorithms—greedy and traversal-based—are designed to convert GNN output probabilities into feasible, non-overlapping allocations.
• The GNN is trained using optimal or near-optimal solutions as labels, enabling the model to learn the structural patterns of high-revenue allocations.
• The method is evaluated on synthetic instances and a real-world VM allocation problem in cloud computing platforms.

Experimental results

Research questions

• RQ1 Can a GNN-based approach achieve near-optimal revenue in multi-unit combinatorial auctions with significantly reduced computational complexity?
• RQ2 How well does the proposed GNN model generalize across different problem sizes and user-type distributions in multi-unit CAs?
• RQ3 Can efficient sample generation processes reduce the need for labeled training data without degrading model performance?
• RQ4 How effective are the proposed graph-based post-processing algorithms in transforming GNN outputs into feasible auction allocations?
• RQ5 Does the GNN-based method outperform traditional solvers like CPLEX and heuristic algorithms in terms of runtime, revenue loss, and resource utilization?

Key findings

• The proposed GNN-based method achieves a revenue gap of only 2.69% to the optimal solution on average, with an average runtime of 20.17 seconds on synthetic instances.
• The method outperforms CPLEX in runtime while maintaining modest revenue loss, demonstrating superior time complexity for large-scale problems.
• The traversal-based post-processing algorithm reduces the number of iterations needed, improving inference speed without sacrificing solution quality.
• The method generalizes well across different user-type distributions, with performance gaps remaining within 3.14% across all tested distributions (e.g., 10%, 40%, 50% and 10%, 30%, 60%).
• The model maintains consistent performance across varying problem sizes, indicating strong generalization capability beyond the training distribution.
• The method shows promise for real-world deployment in cloud computing, particularly for VM allocation, where it balances revenue, efficiency, and user satisfaction.