We address the problem of optimizing over functions defined on node subsets in a graph. The optimization of such functions is often a non-trivial task given their combinatorial, black-box and expensive-to-evaluate nature. Although various algorithms have been introduced in the literature, most are either task-specific or computationally inefficient and only utilize information about the graph structure without considering the characteristics of the function. To address these limitations, we utilize Bayesian Optimization (BO), a sample-efficient black-box solver, and propose a novel framework for combinatorial optimization on graphs. More specifically, we map each $k$-node subset in the original graph to a node in a new combinatorial graph and adopt a local modeling approach to efficiently traverse the latter graph by progressively sampling its subgraphs using a recursive algorithm. Extensive experiments under both synthetic and real-world setups demonstrate the effectiveness of the proposed BO framework on various types of graphs and optimization tasks, where its behavior is analyzed in detail with ablation studies.

翻译：本文研究图节点子集定义函数的优化问题。此类函数因其组合性、黑箱性和评估代价高昂的特性，其优化通常是非平凡的任务。尽管文献中已提出多种算法，但大多具有任务特定性或计算低效性，且仅利用图结构信息而未考虑函数特性。为克服这些局限，我们采用样本高效的黑箱求解器——贝叶斯优化（BO），提出一种新颖的图组合优化框架。具体而言，我们将原始图中每个$k$节点子集映射至新组合图的节点，并采用局部建模方法，通过递归算法逐步采样子图，实现对组合图的高效遍历。在合成与真实场景下的大量实验表明，所提出的BO框架在多种图类型和优化任务中均表现优异，其行为通过消融研究得到了详细分析。