Global Optimization on Graph-Structured Data via Gaussian Processes with Spectral Representations

The recent introduction of a scalable framework for global optimization on graph-structured data marks a significant advancement in Bayesian optimization (BO), which has struggled with the discrete nature of graphs. This new method employs low-rank spectral representations to construct Gaussian process surrogates from sparse structural observations, enabling effective global searches and principled uncertainty estimations even with limited data. The theoretical analysis provided establishes conditions for accurately recovering the underlying graph structure under various sampling regimes. Experiments conducted on both synthetic and real-world datasets demonstrate that this approach achieves faster convergence and improved optimization performance compared to prior methods. This development is crucial for tackling complex optimization problems in various fields, including AI and data science, where graph-structured data is prevalent.