# Bayesian Optimization on Networks

arXiv: https://arxiv.org/abs/2510.27643 · HTML: https://mlsanity.com/paper/2510.27643/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 31 Oct 2025.

## Builds on (most cited first, 18 of 18)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets](https://mlsanity.com/paper/1605.07079/) (2016)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Bayesian Optimization of Combinatorial Structures](https://mlsanity.com/paper/1806.08838/) (2018)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [AI-optimized detector design for the future Electron-Ion Collider: the dual-radiator RICH case](https://mlsanity.com/paper/1911.05797/) (2019)
- [Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration](https://mlsanity.com/paper/2401.17037/) (2024)
- [The rational SPDE approach for Gaussian random fields with general smoothness](https://mlsanity.com/paper/1711.04333/) (2017)
- [The SPDE Approach to Mat'ern Fields: Graph Representations](https://mlsanity.com/paper/2004.08000/) (2020)
- [Optimization on Manifolds via Graph Gaussian Processes](https://mlsanity.com/paper/2210.10962/) (2022)
- [Attentive Neural Processes and Batch Bayesian Optimization for Scalable Calibration of Physics-Informed Digital Twins](https://mlsanity.com/paper/2106.15502/) (2021)
- [Bayesian Optimization with Inexact Acquisition: Is Random Grid Search Sufficient?](https://mlsanity.com/paper/2506.11831/) (2025)
- [Gaussian Process Regression under Computational and Epistemic Misspecification](https://mlsanity.com/paper/2312.09225/) (2023)
- [Guided Bayesian Optimization: Data-Efficient Controller Tuning with Digital Twin](https://mlsanity.com/paper/2403.16619/) (2024)
- [Log-Gaussian Cox Processes on General Metric Graphs](https://mlsanity.com/paper/2501.18558/) (2025)

## Abstract (arXiv)

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Mat'ern Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Mat'ern prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.