What's Wrong With Non-Autoregressive Graph Neural Networks in Neural Combinatorial Optimization

Jerry Sun, Zhixiao Xiong, Chi-Guhn Lee, Eldan Cohen

Keywords: graph neural network, combinatorial optimization, supervised learning

TL;DR: This paper explores the limitations of supervised NAR GNN-based methods for neural combinatorial optimization and introduces a supervised AR framework that better aligns training objectives with solution quality and achieves superior performance.

Abstract: Neural combinatorial optimization (NCO) leverages machine learning models to tackle complex combinatorial problems by learning heuristics or direct solution construction. Graph Neural Networks (GNNs) are particularly effective for NCO due to their ability to capture the relational structure inherent in many such problems. In this work, we examine the supervised non-autoregressive (NAR) solution construction framework, revealing a misalignment between training objective and solution quality. Specifically, through experiments on six GNN architectures across three problems—Traveling Salesperson Problem (TSP), Maximum Independent Set (MIS), and Minimum Vertex Cover (MVC)—we show that lower training loss does not correlate with lower optimality gap. To address this, we propose a supervised autoregressive (AR) framework that leverages the conditional dependencies between variables by training to complete partial solutions. Empirical results show that the proposed AR framework does not exhibit the same misalignment and consistently improves performance. We further compare the proposed AR framework against existing supervised GNN-based methods and achieve superior performance, especially in terms of generalizing to larger problem instances.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 7987