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Bayesian Optimization on Networks

arXiv 2510.27643 ↗First posted 31 Oct 2025stat.ML cs.LG cs.NAcited by 0

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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.

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References · 18

  1. 2018A Tutorial on Bayesian Optimizationcited by 734
  2. 2017On Kernelized Multi-armed Banditscited by 348
  3. 2020On Information Gain and Regret Bounds in Gaussian Process Banditscited by 156
  4. 2016Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasetscited by 131
  5. 2015Bayesian optimization for materials designcited by 78
  6. 2022Recent Advances in Bayesian Optimizationcited by 74
  7. 2018Bayesian Optimization of Combinatorial Structurescited by 64
  8. 2021Misspecified Gaussian Process Bandit Optimizationcited by 52
  9. 2019AI-optimized detector design for the future Electron-Ion Collider: the dual-radiator RICH casecited by 15
  10. 2017The rational SPDE approach for Gaussian random fields with general smoothnesscited by 7
  11. 2024Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Explorationcited by 7
  12. 2020The SPDE Approach to Mat'ern Fields: Graph Representationscited by 6
6 more
  1. 2021Attentive Neural Processes and Batch Bayesian Optimization for Scalable Calibration of Physics-Informed Digital Twinscited by 5
  2. 2022Optimization on Manifolds via Graph Gaussian Processescited by 4
  3. 2025Bayesian Optimization with Inexact Acquisition: Is Random Grid Search Sufficient?cited by 4
  4. 2023Gaussian Process Regression under Computational and Epistemic Misspecificationcited by 2
  5. 2024Guided Bayesian Optimization: Data-Efficient Controller Tuning with Digital Twincited by 2
  6. 2025Log-Gaussian Cox Processes on General Metric Graphscited by 1

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