The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and do not make use of information about the function values; on the other hand, Bayesian optimisation is a class of promising black-box solvers with superior sample efficiency, but it has been scarcely been applied to such novel setups. To fill this gap, we propose a novel Bayesian optimisation framework that optimises over functions defined on generic, large-scale and potentially unknown graphs. Through the learning of suitable kernels on graphs, our framework has the advantage of adapting to the behaviour of the target function. The local modelling approach further guarantees the efficiency of our method. Extensive experiments on both synthetic and real-world graphs demonstrate the effectiveness of the proposed optimisation framework.

翻译：随着图结构数据的日益普及，针对定义在图节点集上的函数进行优化成为重要课题。传统图搜索算法虽可应用于此类问题，但存在样本效率低下且未能利用函数值信息的缺陷；而贝叶斯优化作为一类具有优异样本效率的黑箱求解方法，却鲜少应用于这类新型场景。为填补这一空白，我们提出了一种新颖的贝叶斯优化框架，能够对定义在通用、大规模且可能未知的图上的函数进行优化。通过在图结构上学习合适的核函数，该框架具备适应目标函数行为的优势。局部建模方法进一步保障了方法的计算效率。在合成图与真实图上的大量实验验证了所提出优化框架的有效性。