Bayesian Optimization of Functions over Node Subsets in Graphs

2024-05-24

arXiv.org

AI Summary

This work addresses black-box combinatorial optimization of node subset functions on graphs, where function evaluations are expensive, non-differentiable, and lack analytical structure. Existing methods suffer from poor generalization, low sample efficiency, and failure to exploit graph topology. To overcome these limitations, we propose the first Bayesian optimization framework tailored to combinatorial domains over graphs: (i) we introduce a novel encoding that maps *k*-node subsets to composite graph nodes, thereby constructing a search space explicitly aligned with graph topology; (ii) we integrate local Gaussian process surrogates with a recursive subgraph sampling strategy to enable efficient, structure-aware exploration while preserving functional characteristics. Extensive experiments on diverse synthetic and real-world graph benchmarks demonstrate significant improvements over state-of-the-art baselines (average gain of 23.6%). Ablation studies confirm the necessity of each component. Our framework transcends task-specific design, achieving both strong generalization across graph domains and high sample efficiency.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Graph-based Function Optimization
• Computational Complexity
• Efficiency of Algorithms

Innovation

• Bayesian Optimization
• Mesh Structure Graphs
• Recursive Sampling