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：图结构数据的日益普及推动了对图节点集上定义函数进行优化的任务。传统的图搜索算法可应用于此类场景，但可能样本效率低下且未利用函数值信息；另一方面，贝叶斯优化是一类具有优越样本效率的黑盒求解器，但鲜少被应用于此类新颖设置。为填补这一空白，我们提出了一种新颖的贝叶斯优化框架，用于优化定义在通用、大规模且可能未知的图上的函数。通过学习图上的合适核函数，我们的框架具有适应目标函数行为的优势。局部建模方法进一步保证了我们方法的效率。在合成图与真实图上的大量实验证明了所提优化框架的有效性。