The Winner Determination Problem (WDP) in combinatorial auctions is NP-hard, and no existing method reliably predicts which instances will defeat fast greedy heuristics. The ML-for-combinatorial-optimization community has focused on learning to \emph{replace} solvers, yet recent evidence shows that graph neural networks (GNNs) rarely outperform well-tuned classical methods on standard benchmarks. We pursue a different objective: learning to predict \emph{when} a given instance is hard for greedy allocation, enabling instance-dependent algorithm selection. We design a 20-dimensional structural feature vector and train a lightweight MLP hardness classifier that predicts the greedy optimality gap with mean absolute error 0.033, Pearson correlation 0.937, and binary classification accuracy 94.7\% across three random seeds. For instances identified as hard -- those exhibiting ``whale-fish'' trap structure where greedy provably fails -- we deploy a heterogeneous GNN specialist that achieves ${\approx}0\%$ optimality gap on all six adversarial configurations tested (vs.\ 3.75--59.24\% for greedy). A hybrid allocator combining the hardness classifier with GNN and greedy solvers achieves 0.51\% overall gap on mixed distributions. Our honest evaluation on CATS benchmarks confirms that GNNs do not outperform Gurobi (0.45--0.71 vs.\ 0.20 gap), motivating the algorithm selection framing. Learning \emph{when} to deploy expensive solvers is more tractable than learning to replace them.

翻译：组合拍卖中的胜者确定问题（WDP）是NP难问题，现有方法无法可靠预测哪些实例会击败快速贪心启发式算法。组合优化机器学习领域的研究一直聚焦于学习如何替代求解器，但近期证据表明，在图标准基准测试中，图神经网络（GNN）很少能超越经过良好调优的经典方法。我们追求一个不同的目标：学习预测特定实例何时对贪心分配算法构成困难，从而实现实例依赖的算法选择。我们设计了一个20维结构特征向量，并训练了一个轻量级多层感知机难度分类器，该分类器在三个随机种子下预测贪心最优性间隙的平均绝对误差为0.033，皮尔逊相关系数为0.937，二元分类准确率达到94.7%。对于被识别为困难的实例——即那些表现出“鲸鱼-小鱼”陷阱结构（贪心算法可证明会失败）的实例——我们部署了一个异构GNN专家模型，在所有测试的六种对抗性配置上实现了约0%的最优性间隙（相比之下贪心算法的间隙为3.75%–59.24%）。一个结合了难度分类器、GNN和贪心求解器的混合分配器，在混合分布上实现了0.51%的整体间隙。我们在CATS基准测试上的诚实评估证实，GNN并未超越Gurobi（间隙为0.45–0.71对比0.20），这支持了算法选择框架的合理性。学习何时部署昂贵的求解器比学习替代它们更为可行。