mlsanityData to 14 Oct 2026

Optimization on Manifolds via Graph Gaussian Processes

arXiv 2210.10962 ↗First posted 20 Oct 2022stat.ML cs.LG math.OCcited by 6

Not on the map. Why?

Abstract (arXiv)

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 31 of its 68 references that are in the map. First posted on arXiv 20 Oct 2022.

Builds on

31 of 68 references.

References · 31

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19 more
  1. 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
  2. 2019Bayesian Optimization Meets Riemannian Manifolds in Robot Learningcited by 23
  3. 2021Bayesian Optimization over Hybrid Spacescited by 23
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  5. 2018Inverse Problems and Data Assimilationcited by 18
  6. 2019Optimization on flag manifoldscited by 13
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  8. 2018Gaussian Process Landmarking on Manifoldscited by 9
  9. 2017The rational SPDE approach for Gaussian random fields with general smoothnesscited by 7
  10. 2020The SPDE Approach to Mat'ern Fields: Graph Representationscited by 6
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  12. 2017On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithmscited by 5
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  14. 2017Continuum Limit of Posteriors in Graph Bayesian Inverse Problemscited by 4
  15. 2020Unlabeled Data Help in Graph-Based Semi-Supervised Learning: A Bayesian Nonparametrics Perspectivecited by 4
  16. 2022Manifold Free Riemannian Optimizationcited by 4
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  18. 2021Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundariescited by 2
  19. 2022Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learningcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 2.

6 papers.

  1. 2024Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Explorationcited by 8
  2. 2025Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector designcited by 2
  3. 2025Active Learning for Manifold Gaussian Process Regressioncited by 0
  4. 2025Bayesian Optimization on Networkscited by 0
  5. 2026A Representation Optimization Dichotomy, Lie-Algebraic Policy Optimizationcited by 0
  6. 2026Exploration strategies for Gaussian process bandit optimization with inference regret guaranteescited by 0