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Learning Structural Hardness for Combinatorial Auctions: Instance-Dependent Algorithm Selection via Graph Neural Networks
[Submitted on 16 Feb 2026 (v1), last revised 24 Jun 2026 (this v · 2026-06-25 · via cs.LG updates on arXiv.org

This paper has been withdrawn by Sungwoo Kang

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Abstract: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.

Submission history

From: Sungwoo Kang [view email]
[v1] Mon, 16 Feb 2026 14:26:25 UTC (101 KB)
[v2] Wed, 24 Jun 2026 08:19:42 UTC (1 KB) (withdrawn)

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