Bayesian Optimization of Functions over Node Subsets in Graphs

TL;DR

This paper introduces a Bayesian Optimization framework tailored for efficiently optimizing functions over node subsets in graphs, addressing the combinatorial complexity and computational challenges of such tasks.

Contribution

It proposes a novel graph mapping and local modeling approach for combinatorial optimization, improving efficiency and effectiveness over existing methods.

Findings

Effective on synthetic and real-world graphs

Outperforms existing algorithms in efficiency and accuracy

Provides detailed analysis and ablation studies

Abstract

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.