基于图神经网络的多单元组合拍卖中标者快速确定方法
A Fast Graph Neural Network-Based Method for Winner Determination in Multi-Unit Combinatorial Auctions
摘要：
组合拍卖是一种有效的资源分配机制，适用于包括云计算在内的不同领域。它允许投标人就不同项目的组合而不是仅就单个项目提交投标，从而可以获得高经济效益和用户灵活性。然而，如何在投标人之间分配物品以使拍卖人的收益最大化，即，获胜者确定问题（WDP）是NP完全问题，并且是不可逼近的。现有的WDP的工作一般是基于数学优化技术，其中大多数集中在单单元WDP，其中每个项目只有一个单元。相反，很少有作品考虑多单元WDP中，每个项目可能有多个单位。鉴于多单元WDP更复杂，但在云计算中很普遍，我们建议利用机器学习（ML）技术来开发一种新的低复杂度算法来解决这个问题，收入损失可以忽略不计。具体来说，我们建模的多单元WDP作为一个增强的二分投标项目图，并使用半卷积运算的图神经网络（GNN）学习的概率，每个出价属于最优分配。为了提高样本生成效率，减少所需的标记实例的数量，我们提出了两种不同的样本生成过程。我们还开发了两种新的基于图的后处理算法，将GNN的输出转换为可行的解决方案。通过对云计算平台上的合成实例和特定虚拟机（VM）分配问题的仿真，验证了该方法能够以较低的复杂度逼近最优性能，并在问题规模和用户类型分布方面具有良好的泛化能力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
