There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node. To further facilitate the combinatorial nature of the problem, GCOMB utilizes a Q-learning framework, which is made efficient through importance sampling. We perform extensive experiments on real graphs to benchmark the efficiency and efficacy of GCOMB. Our results establish that GCOMB is 100 times faster and marginally better in quality than state-of-the-art algorithms for learning combinatorial algorithms. Additionally, a case-study on the practical combinatorial problem of Influence Maximization (IM) shows GCOMB is 150 times faster than the specialized IM algorithm IMM with similar quality.

翻译：通过机器学习,人们越来越有兴趣发现图表中组合问题的外观。虽然现有技术主要侧重于获得高质量的解决方案,但尚未充分解决可扩缩到10亿大小的图表的问题。此外,对于许多实际情景所必需的预算限制的影响仍有待研究。我们在此文件中提议了一个称为GCOMB的框架,以弥补这些差距。GCOMB用一种新颖的、具有概率的贪婪机制来预测结点的质量来培训一个图表革命网络(GCN )。为进一步促进问题的组合性质,GCOMB使用一个Q学习框架,通过重要取样提高效率。我们在实际图表上进行了广泛的实验,以衡量GCOMB的效率和效能。我们的结果表明,GCOMB在质量上比学习组合算法的最先进的算法快100倍,质量略高一点。此外,关于影响最大化(IM)的实际组合问题的案例研究显示,GCOMB比专门性IM 算法质量要快150倍。