BoGrape: Bayesian optimization over graphs with shortest-path encoded

Yilin Xie, Shiqiang Zhang, Jixiang Qing, Ruth Misener, Calvin Tsay

Keywords: Bayesian optimization, graph optimization, mixed-integer programming, shortest-path

TL;DR: We introduce Bayesian optimization for functions over general graph spaces by encoding shortest-paths in mixed-integer programming.

Abstract: Graph-structured data are central to many scientific and industrial applications where the goal is to optimize expensive black-box objectives defined over graph structures or node configurations---as seen in molecular design, supply chains, and sensor placement. Bayesian optimization offers a principled approach for such settings, but existing methods largely focus on functions defined over nodes of a fixed graph. Moreover, graph optimization is often approached heuristically, and it remains unclear how to systematically incorporate structural constraints into BO. To address these gaps, we build on shortest-path graph kernels to develop a principled framework for acquisition optimization over unseen graph structures and associated node attributes. Through a novel formulation based on mixed-integer programming, we enable global exploration of the combinatorial graph domain and explicit embedding of problem-specific constraints. We demonstrate that our method, BoGrape, is competitive both on general synthetic benchmarks and representative molecular design case studies with application-specific constraints.

Primary Area: optimization

Submission Number: 13126